It doesn't sound like a great relationship. I am quite certain he has some good qualities, otherwise you wouldn't want to continue the relationship.

I was also in a relationship with a man who drank heavily. It did not end well.

Unless he is motivated to change drinking or anything, really, he isn't going to change. You can't fix him. I am sorry I cannot be more positive about the future of your relationship with him but my experience says to leave now and don't waste more of your life in a bad relationship.