Is it allowed, in badminton (mix) doubles, to use your partner to gain more height in order to perform a jump smash for example?
Presumably you mean by, say lifting your partner in the air.
I don't think there's any rule which would ban this.
However, I doubt that it would be effective in practice as the game is so fast and you'd only know where the shuttle is going at the last second. Also, as there are only two of you on the court, you may struggle to lift your partner without dropping your racket.
Contrast this with a Rugby Lineout, where a lighter player may be surrounded by several stronger players with their hands free.