Should I be mad at him? Should i side with my mom?

Okay so my husband lives with me and my parents. until we can get a place of our own we are stuck living with them. and living with my mom is pretty exhausting and he absolutely hates living with her, he doesn't hate her he just disagrees with about everything she says. So my husband usually works 5pm- 10pm or 3-10pm shifts. and he usually gets 2 days off. He works at Target. So we just had a baby and my mom is telling me that he doesn't let me sleep enough, i mean i get mad at him a lot when he doesn't wanna help with the baby but he's getting better. I usually stay up with the baby until 4 in the morning and he stays up from 4-8 (we get sleep when we can inbetween our shifts and when baby is sleeping. and when he has to work early in the morning i stay up with baby all night) well he usually goes back to sleep and doesn't help me take care of him when he wakes up. usually doesn't have to be at work until 5 so he plays games and just messes around and what not while i care for the baby. I'm not mad at him because he is supporting us atm. My mom thinks i'm not standing up for myself because i dont tell him i want more sleep. i mean i'm at home all day i don't have a job yet. should i be mad at him for not allowing me as much sleep as he gets? should i listen to my mom or should i just butt her out considering she tries so hard to get into our lives and how we raise the baby. It's not her baby. so i see why Drew doesn't get along with her but i really feel like i shpuldnt be on her side about everything (which i am more than i should) i know i need to stick up for my husband. am i right!?