Sorry to tell you this but it's going to get worse, much worse if he doesn't admit he's an alcoholic and if you don't start getting help. I've been where you are at and now I am dealing with the I guess 7 years of wasted time that I posted here asking the same types of questions and riding along the "cutting down" conversations, broken promises, fights etc.
I'm still learning just like you. My husband is sober almost 60 days (30 days were rehab) and now we are in a different kind of h&ll trying to sort through the wreckage. I'm hopeful we can make it through this but I don't know. A lot has been done. You're thread is titled Should I Believe He'll Change? Currently? What what you have shared? Not for a single second should you believe he will change. Keep posting here it's helped for me. I have been where you are at and I am praying for you.