DH is a night owl and I'm an early bird.
When DS was a baby he would have a feed around midnight to 1am and then again around five am.
I did try and do the midnight feeds initially but it was almost impossible. I was so tired, I'd struggle to stay awake and quite often I'd sleep through DS cries whereas DH would wake (or still be awake) every time and help me set up the bottle etc.
Whereas he would sleep through the 5am feed being completely oblivious to it all and I'd be wide awake.
So in the end he ended up doing the late feed and I did the early morning one.
I've since got a Fitbit and it has shown that the midnight hour is when I'm in my most deepest sleep. I never really stood a chance.
Even now, 9 years and a second DC later, DH is still the one who gets up in the middle of the night to attend to bad dreams, lost teddies etc whilst I'm comatose, and I'm still the one who gets up at the crack of dawn with them.
You need to find a solution that works for both of you, otherwise it's just going to breed resentment.