There is so much to unpack here. Yes, it can get better but you and your husband need to be on the same page for anything to work. First suggestion is therapy.

Second suggestions is that unless your baby has a health condition that you need to be next to it at night, I would start transitioning them to their own room and start sleep training.

So who’s idea was it that since he had weird hours, he was absolved if night parenting duties? That is some bullshit. You both made a baby and he can’t unilaterally decide that his time/sleep is more precious/valuable than yours. It’s time that you take back your life from these stupid gender roles that make it so difficult to be a mom. Why does he have a 40-50hr work week, but you are expected to be on call 24/7? The thing is that technically you both have a 24/7 job of taking care of that baby and one person is being subordinate.

If I were you, I would take a two night break every 3 weeks. Just drop everything, get a hotel room or go to a friends/parents house and take some you time. If you breastfeed, pump in preparation. That is the unilateral decision you get to make. I promise real quick, he will get tired of that arrangement and meet you in the middle at night.

Me and my DH had routine with both of our kids- that he would get up, change the baby and bring them to me for me to feed, then I put them back to bed. If there were times that one of us needed a whole night, the other would cover it with the assumption that the following night was the other’s turn for a full night. We learned that a tit for tat way of handling nights was the way toward the least amount of resentment towards each other.