Hi, would it be better if he didn't live with you? It doesn't sound like a lifestyle that's suitable for children to see.
He's kidding himself, as A's do, about the extent of his problem, because if he considered it seriously he'd have to do something about it.
At the moment he's not contributing much to your partnership on an emotional level, and I'm guessing you're carrying most of the load around the house and with the finances. In that sense, his alcoholism is a problem for you, if not for him.
You won't be able to make him stop drinking, because unless he's convinced himself that it's necessary his half-arsed attempts will always fail. So the decision you're left with is how it impacts your life, and what your bottom line is.
I thing Al-anon (for the families, not the alcoholic) would be a great first step.