Formula will not make your baby sleep better.
My LO only gets breastmilk and sleeps from 7:30-2 am or later every day - and then sleeps from 2:20 (approx-she eats then goes back to sleep) until 6:30 or 7.
I do not know how to address your DH not wanting to learn how to be a father. I have learned that my DH does a lot better when he is alone with her and I am not there for back up - if I am home, he tends to come to me, but if I am not there, him and LO do just fine on their own. However, he has been giving her bottles since she first needed one when she was 2 days old, and helped me sleep early on by giving her a bottle of pumped milk while I slept when she was still waking every 2-3 hours to eat (just one a day; I did the night feedings after that).
It sounds like either your DH needs to start accepting some parenting responsibilities or you need to find someone else to watch LO.
I usually do bedtime but Lo will go down for DH if he gives her a bottle instead.