I'm not going to leave him, I don't see how that is going to help anything.
It will help you. You are responsible for making decisions that are in your best interest. No one else can do it.
How is staying with an alcoholic the best thing for you?
The thing is - staying isn't going to help him either. It just isn't. It is not going to make any difference at all to his drinking. LexieCat pointed out that if he was really serious about recovery, he'd step away from the relationship himself.
I would encourage you to read some of the stickies at the top of the forum. They are chucked full of insight.
You asked what you are supposed to do. I suggest that you find an al-anon meeting. The Al-Anon Family Groups are a fellowship of relatives and friends of alcoholics who share their experience, strength, and hope in order to solve their common problems.
Stick around, there are a lot of wise souls here. I have learned so much from reading here.
FWIW I married a harmless drunk. I learned some things over the years. I can give you tips on how to hide your money, your child's allowance, your checkbook, how to clean up bodily fluids, how to avoid social gatherings, how to detach and not talk to the man you share a life with, how to sneak to bed to avoid him, how to lie to friends and relatives, how to perfect the art of nodding and ignoring, how to cry in the shower, how to pretend there isn't someone passed out in your recliner most nights, how to decline invites from neighbors, how to smile with your mouth and not your eyes, how to 'help' someone until the enabling became so complete we both hated both of us. I can show you what that looks like after a few years. A broken, depressed, exhausted, emotionally dead, rigid, lifeless, controlling, confused, shell of a woman so filled with resentment and rage she could no longer function. I doubt those are the kinds of tips you were hoping to hear but that is what living with a harmless drunk for 16 years is like. I won't start with what it has done to four innocent children.