Also, I want to support him to find a job, as this, I feel, is one of the keys to him getting better.
Commendable sentiment but there's nothing you can do or say to affect an alcoholic's drinking. You're seeing this as a cause and effect proposition: "if he had a job........", "if our marriage worked.......", he would stop drinking. He gets falling down drunk for one reason: he's an alcoholic.
He may get sober but that's on him. As a recovering alcoholic (27 years) I've never heard anyone say they got sober because of another person, a job, children, family/friends. He/she stops when the pain becomes too much or they have a scare (I almost died in a blackout). So take care of yourself, it's time for him to deal with the consequences of his actions and words.