He's "sober, but not attending AA" - which means he won't be sober for long.
My feeling is that your husband is still quite the alcoholic....my guess is that if he isn't secretly drinking, he will be openly drinking very soon. Four months is a wisp of a moment in sobriety, and as you say, he was an alcoholic for a long time.
Wanting, honey, you know exactly what he is doing with the single girls until 4AM, no matter WHAT he says (LIES) or who he blames (YOU).
I'm positive he's not cheating (in the technical sense) and I'm positive he's not drinking.
It's hard to imagine him actually drinking again.
Guess what? He was cheating on me.
And he is now drinking again.
I don't think I can ever rule anything out when it comes to his behavior. I found out that he had a thing with one girl since I was pregnant 4 years ago. And now he wants one of his girlfriends to play house with our kids. Insane.