I want to settle the issue with the jump attack once and for all.

Quote from ColinRosso >>

 is it possible to perform an attack while jumping without interrupting the jump itself?

 It depends. Attacks can be performed at any time during your Move, so if you are jumping as part of your move you definitely can attack during that jump. However, there are some abilities that give the ability to jump as a Bonus Action. There is no rule about interrupting a bonus action with an attack thus RAW you could not attack as part of or during a jump you make as a Bonus Action. However, DMs might decide to allow attacks during the latter to make the in-game logic more consistent but there is no guarantee - IMO this ruling would make sense because technically there is no rule allowing you to make an attack during a Rogue or Monk's Bonus Action Dash action but I don't know any DM that runs the game that way, so if you would allow a Monk or a Rogue to make attacks during a bonus action Dash, you should also allow attacks during a bonus action jump. 

That said, there is also a blanket rule that the DM may give you Disadvantage on a roll if your character is for whatever reason hampered in the thing they are attempting. It is certainly reasonable to rule that trying to swing a sword or fire a bow in the middle of a high / long jump would be significantly more difficult than normal and thus rule that such attacks are made with Disadvantage.

Quote from up2ng >>

just like how if you Fall a certain distance that entire fall would be resolved immediately.

 Why would that happen? This is not RAW. RAW falling can continue over multiple turns if the distance you are falling is long enough, so things absolutely can happen during a fall it is not resolved instantaneously. Notably featherfall can be cast as a reaction at any point while a creature is falling, it does not have to happen the moment a creature begins to fall. For instance, if a character falls from a high building and there are cloth roofs blocking the caster's vision of the falling creature the caster can still cast Featherfall on the falling creature mid-fall once it has ripped through the roof so the caster has line-of-sight.

Quote from Agilemind >>

Quote from up2ng >>

just like how if you Fall a certain distance that entire fall would be resolved immediately.

 Why would that happen? This is not RAW. RAW falling can continue over multiple turns if the distance you are falling is long enough, so things absolutely can happen during a fall it is not resolved instantaneously. 

Nope.  That does not happen under the standard default rules.  There is an optional rule that was published in Xanathar's Guide to Everything which did that for extremely long falls, but not everyone uses that book.

Falling (Rules Glossary):

Falling [Hazard]

A creature that falls takes 1d6 Bludgeoning damage at the end of the fall for every 10 feet it fell, to a maximum of 20d6. When the creature lands, it has the Prone condition unless it avoids taking any damage from the fall.

From Xanathar's Guide to Everything:

Falling

Falling from a great height is a significant risk for adventurers and their foes. The rule given in the Player’s Handbook is simple: at the end of a fall, you take 1d6 bludgeoning damage for every 10 feet you fell, to a maximum of 20d6. You also land prone, unless you somehow avoid taking damage from the fall. Here are two optional rules that expand on that simple rule.

Rate of Falling

The rule for falling assumes that a creature immediately drops the entire distance when it falls.  But what if a creature is at a high altitude when it falls, perhaps on the back of a griffon or on board an airship? Realistically, a fall from such a height can take more than a few seconds, extending past the end of the turn when the fall occurred. If you’d like high-altitude falls to be properly time-consuming, use the following optional rule.

When you fall from a great height, you instantly descend up to 500 feet. If you’re still falling on your next turn, you descend up to 500 feet at the end of that turn. This process continues until the fall ends, either because you hit the ground or the fall is otherwise halted.

Flying Creatures and Falling . . . [another optional rule that involves flying creatures] . . .

Quote from Agilemind >>

Notably featherfall can be cast as a reaction at any point while a creature is falling, it does not have to happen the moment a creature begins to fall. For instance, if a character falls from a high building and there are cloth roofs blocking the caster's vision of the falling creature the caster can still cast Featherfall on the falling creature mid-fall once it has ripped through the roof so the caster has line-of-sight.

While it is reasonable for a DM to rule that spell in this way, mechanically, it doesn't work like that.  Here is the wording for the trigger for Feather Fall, which targets "up to 5 falling creatures":

Casting Time: Reaction, which you take when you or a creature you can see within 60 feet of you falls

This verb indicates the exact moment when a creature transitions from "not falling" to "falling" which is indeed the moment a creature begins to fall.  The same word is used in the rule for Falling so this same moment is the trigger for two things simultaneously.  It triggers the resolution of the fall, which resolves instantly.  It also triggers the Reaction for the Feather Fall spell such that the fall resolves differently.

Quote from Agilemind >>

Attacks can be performed at any time during your Move, so if you are jumping as part of your move you definitely can attack during that jump. However, there are some abilities that give the ability to jump as a Bonus Action. There is no rule about interrupting a bonus action with an attack thus RAW you could not attack as part of or during a jump you make as a Bonus Action. However, DMs might decide to allow attacks during the latter to make the in-game logic more consistent but there is no guarantee - IMO this ruling would make sense because technically there is no rule allowing you to make an attack during a Rogue or Monk's Bonus Action Dash action but I don't know any DM that runs the game that way, so if you would allow a Monk or a Rogue to make attacks during a bonus action Dash, you should also allow attacks during a bonus action jump. 

 

A lot of this is not really how these mechanics work.

First, perhaps you could give an example of jumping as a Bonus Action?  In general, jumping is a mode of movement, it doesn't consume your action or Bonus Action.  For example, the Jump spell costs a Bonus Action to cast.  The effect of that spell is that it allows a creature to perform an enhanced jump on its turn with a certain movement cost.  When that creature actually executes that jump, doing so does not require a Bonus Action, it requires a certain amount of movement.  None of this discussion is about "interrupting a Bonus action".

The movement rules in question say that you can break up your move -- you don't generally break up your action or Bonus action or Reaction.  You don't generally move at all during your action or Bonus action or Reaction -- the notable exception being the Attack action which explicitly allows for movement between attacks during that action.

Breaking Up Your Move

You can break up your move, using some of its movement before and after any action, Bonus Action, or Reaction you take on the same turn.

The question in this thread is:  Are you allowed to "break up" a Jump.  The general rule is that you can "break up your move" (see above).  But what about the specific rule for the Jumping mode of movement?  Does the wording for that specific rule override the above general rule and disallow breaking up this particular movement?  In my opinion, it does:

When you jump, you make either a Long Jump (horizontal) or a High Jump (vertical).

When you make a Long Jump, you leap horizontally a number of feet . . .

In my opinion, when "you make" a Long Jump or a High Jump, that jump gets resolved.  Just like when "you make" an attack, that attack gets resolved.

As for making an attack "during" a Rogue's Bonus action Dash -- again, it doesn't actually work like that.

When you take the Dash action, you are just adding to the amount of movement that you can use for that turn.  When you actually use that movement, you are using your movement, not your Bonus Action.  This movement actually occurs after your Bonus action, which is allowed by the above rule for Breaking up Your Move.

Dash [Action]

When you take the Dash action, you gain extra movement for the current turn.

Quite frankly, this is one of the easiest and most obvious Rule of Cool calls a DM can make. If you meet a DM that won't let you do this because they don't think it's RAW, it might be a good idea to search for a new DM. Because it really takes someone with absolutely no concept of "fun" to seriously consider disallowing this.

When you fall from a great height, you instantly descend up to 500 feet. If you’re still falling on your next turn, you descend up to 500 feet at the end of that turn. This process continues until the fall ends, either because you hit the ground or the fall is otherwise halted.

See emphasis above. Falling can continue across multiple turns, therefore you can absolutely take actions and bonus actions during a fall.