Get out of this. It will not get better anytime soon. It will be a bad situation for you and your baby. He will not help you with the baby, he will only make it harder to raise the baby peacefully. I mean, do you want him to watch the baby while you sleep? Do you think he'd be good alone with a baby? Imagine the scene of finally getting a colicky baby off to dreamland after hours of rocking and having him come in the room, drunk and yelling and turning on all the lights! This is the kind of thing that will happen.
Alcoholism turns nice people into unrecognizable monsters. My ex LOVED his son so much, they were like two peas in a pod. Once my ex became an alcoholic, he changed completely. He now only rarely sees his son and breaks dates with him, etc. He can only be with our son supervised, but even supervised it's not a good situation because he cries and complains to my son all the time (it's like my son is the parent), and he only hangs out with my son for a very short while before he gets bored and leaves, etc. If your guy is currently an alcoholic, and he no doubt is, he is incapable of being a good parent right now. Maybe he will get sober someday, but maybe not and your kid deserves more. Let him try to get sober on his own, you don't need to drag the kid through this.
Sorry if I sound too definite about the fact that you must leave, but I just know how this is going to go and I hope that you will not be another statistic.