It does sound like he is trying. Likely doing the best he can. Since you're still in, (not done) why not attempt to guide him along into being the H you want? Wouldn't it be wonderful if he surprised you?!
He already knows OW is the main issue for you. Good job voicing that in your session!
I know my W has man friends that she tells me about, and I also know there is nothing inappropriate going on between them... she's very open about it, and they only have very intermittent contact... not the silly round the clock nonstop contact of a true EA or PA. We live together, I know these things. Your situation may vary, I have not kept up with the details of your sitch or H's relationship with OW.
Unless it's an absolute a deal breaker for you, maybe you could look at his texts occasionally. Or ask him questions about what they are talking about. (preferably right after their contact, when it is fresh) If he's serious he'll jump at the chance to open up to you, and you'll have a better sense of what's really going on. Then you'll have more facts to help guide your next move, whatever that may be.
M: A really long time. Crisis: 5 years. She's still worth it.
Life is never made unbearable by circumstances, but only by lack of meaning and purpose. -Viktor Frankl
