What made you see that you behavior was wrong? H doesn't see it yet. He still sees it as me trying to control him.
My wife started texting/chatting with an old "friend". She did the same thing I did, she started sharing marital problems. She enjoyed talking to him more than me, she shared things with him she wouldn't tell me, etc. Only difference was they started sexting each other.
Before I knew my wife had an EA with the guy I already began to see why it hurt her when I talked to my friend. She wanted me to be the person I talked to, enjoyed talking to, shared things with. I just didn't get it until the tables were turned.
However, I definitely don't think that's how anyone should play it. Jealousy begetting jealousy is not a recipe for marital success. I think you need to establish clear boundaries, and if he violates them, enforce the consequences. Like I said, the only thing I can think of that would have shocked me into reality was her leaving. At that point I would have had to confront that I was choosing someone over my decision to stay with her. Also, my friend would have stopped talking to me (because she was a really good friend) if she knew it would have ended it.
In my case, walking out was the only thing that stopped my wife from going further with her EA. She was planning to fly out and have a weekend sex fest with the guy until I walked out, then she realized that what she was doing was threatening her entire life. However, up to the point of me walking out, I had no idea how far it had gone. She was still telling me they were "just friends."
Your husband and this woman have a connection, he's either lying to you about it or he's not being honest with himself. Don't let him set the boundary, you need to set it, and stick to the consequences. I don't want to say he's an A**hole, because like I said, I did the same thing and I definitely loved my wife, but he needs a nice kick in the brain for sure. And I can tell you that this forum is filled with stories like yours where the woman stayed and tolerated it and it ended poorly.
This will not get better on it's own. It will only get worse. Deal with it now.