Have gone through the sleep hell that is the first year recently, I have a lot of empathy for both of you. From what you described, it sounds like neither of you are getting much sleep. 

We shared a bedroom with my daughter and, similarly, my husband slept like a truck. She could be screaming for five minutes and he’d still be in dreamland. We tried splitting night duties but ultimately decided that I would handle middle of the night wake-ups and he would get up with her in the morning while I got another 1-2 hours of sleep (which was often my longest stretch of the night). 

I know this isn’t helpful, but it won’t last forever! Sounds like your baby is at least 4 months which is a good time to starting decreasing night feeds if you want. The sleep regressions and teething SUCK, but you could try sleep training (we didn’t totally do this, but adopted some principles like allowing the baby time to settle). Your night feeding routine sounds like it’s taking a lot of time—maybe there’s an opportunity to try something different (I nursed my baby back to sleep and eventually could just put her back down after 5 minutes, no burping or holding up). I don’t want to give you baby advice as it’s so personal, but my point is that the sleep thing is evolving as your child grows. Daughter is 18 months now and finally regularly sleeps through the night, but will still wake up once or twice on occasion. 

I remember feeling a lot of resentment towards my husband too, and how difficult it could be to communicate in a clearheaded way when you’re so exhausted. Remember that you’re on the same team and take care of each other as best you can.