Alchoholism does not need to be diagnosed. He is an alcoholic. You know this. Don't question it. It doesn't matter if anybody else thinks he is or isn't. All that matters is it's a problem for you.
Something for you to investigate is why you chose two alcoholics in a row as boyfriends, and married one of them. Al-Anon is a good place to do this.
How to find a meeting in the US/Canada/Puerto Rico
Take care and good luck,
Cyranoak