On a long rest you recover half your hit dice (rounded down) how does this work with multiclass, are the hit dice for each class dealt with the same or seperately?

Say you are at level 6:  Fighter 3, Rogue 3. 

If you have used all your hit dice do you get 1d10 and 1d8 back or 3 hit dice (if so which ones?)

If you have used your 3 d8s how many do you get back?

Does it work differently if your two classes have the same size hit dice, if you are say rogue 3 monk 3 and have used all your hit dice do you get 3 back even if the fighter 3 / rogue 3 only gets 2?

I'd just give them back half their total level, starting with the biggest hit dice. I see no reason not to just do what's most advantageous for them.

They get back any three of their six hit dice that they choose.

The character also regains spent Hit Dice, up to a number of dice equal to half of the character's total number of them (minimum of one die).

The rule is based on character hit dice, not class hit dice, so if they are a 3/3 split multiclass, they get up to 3 dice of their choice back.

The real question should be whether to round up or down, since I don't see that in the rule anywhere (other than "min 1"). I'd rule to round up.

Quote from DxJxC >>

The character also regains spent Hit Dice, up to a number of dice equal to half of the character's total number of them (minimum of one die).

The rule is based on character hit dice, not class hit dice, so if they are a 3/3 split multiclass, they get up to 3 dice of their choice back.

The real question should be whether to round up or down, since I don't see that in the rule anywhere (other than "min 1"). I'd rule to round up.

 In D&D5e, unless specifically stated otherwise you always round down.