Rant: my husband is no help at all!

I get that my husband works 3rd shift but he still has to be the laziest person I’ve ever met in my life. I prayed it would change after our son was born but it hasn’t. I’m home alone with my son all night and during the day my husband sleeps so it’s mainly me taking care of him. When my husband finally gets up he’s still no help at all. He huffs and rolls his eyes every time I ask him to help me with anything. He falls asleep as he’s feeding our son and lets the bottle fall out of his mouth and formula gets all over him. He’s about let him fall out of his arms repeatedly because he dozes off. There’s been multiple times he’s told me to get some rest but when I go to check on them my son is crying and my husband is passed out. This even happens when he’s had the night off. He’s even nodded off while driving when we were in the car with him. I’m at my wits end! It’s to the point I don’t let him out of my sight when he’s holding our son. I yell for him to wake up and he always denies it even though I’ve watched him do it. Then he gets so angry with me about it. I’ve also noticed he gets an attitude with our son really bad and he’s only 8 weeks old. I’ve had to tell him to stop being so hateful to the baby because he doesn’t understand. When I finally go off he cries and says he’ll do better but within a week it’s right back to the same thing. I could deal with it before our son was born but now it’s on both of us to raise our son. I really think if things don’t change it could ruin our marriage. How can I continue to be with someone who I can’t even trust with our child? He is so selfish and so neglectful that he would rather him get 12 hours of sleep than help me or spend time with our son.