Any advice would be appreciated

I’m married but feel like a single parent. My husband doesn’t spend much time with our daughter. I feel like the only times he wants to is to relieve me so I can eat or maybe nap for a little. When he does he’s usually always on his phone or playing a game. I want him to be more of an active parent and read to her or something. I always feel like he’s in a rush and wants to do other stuff. He seems more concerned about gaming. Besides all this he has not much patience and a bit of a temper. I’ve caught him in some lies and I’m just getting tired of it. I feel stuck with this quarantine because not like I could go to my parents or take any type of action. I’m curious if anyone else’s husband has the same behaviors or doesn’t equally share in parental duties. What would you do?? We have two somewhat large fights. One the other week and one in February. He has pretty bad depression and won’t do anything to help himself. Doesn’t want to go to counseling and doesn’t take his medicine (that he lied and said he was taking) also told me he had stopped smoking when he hadn’t. Our daughter was in the hospital as well for a few days and I stayed the night every night and he could barely be there more than a few hours and said he was too stressed and went home.