Jessica,
Welcome to SR, I am sorry that you are here.
I wish 34 years ago when I started dating AXH that I had listened to my red flags, like you are. I kept telling myself that I could hand anything. Well, I couldn't. What I did not understand was, that alcoholism is progressive. Today and tomorrow you can handle it, its long term affects and hard ache on you, is what takes a toll.
Like Anvil said, does having a title on it mean anything. You have an issue with his drinking, he acknowledged his drinking, what more do you need. So the question is, how do you move forward? You can read around the f & f forum and see all the pain us enablers feel. Alcoholism is a family disease, it does not only affect the addict. Take your time, educate yourself and make a sound decision on what you need to do for your future.
Sending hugs my friend, I know it hurts and you love him. We all love our addicts, but love does not "fix" alcoholism.