Thank you for bringing your question to Just Answer!
You know you're not getting a truthful answer from him about this woman. If she has a boyfriend, there's very little chance that she would be calling him after midnight...or that she would need to lean on him when she has a boyfriend.
You know he has a commitment problem, and most likely, a history of cheating. Even though you have feelings for him, he's a poor risk for a husband. If he's doing this now, when he should be on his best behavior, imagine how much more he will do it if you ever got married and he can take you for granted.
He knows how much this hurts you, yet he refuses to make it stop. Is this how you picture your husband treating you? During the first year or so of a relationship, you're seeing a man at his best. This-- how he's acting right now--is as good as it's ever going to be.
A man in love puts his partner's feelings first. He's not doing that. Think about choosing someone instead who devotes himself to making you feel secure, loved, and cherished.
A person doesn't--and can't--change his personality because someone asks him to. He is who he is...and he's going to waste a lot of your time while he's "working" on something he can't change without a lot of intensive therapy (his inability to commit).