Toothpaste, I think that those "lot of people" who are still in love with their first loves need some damn therapy, and shouldn't be inflicting themselves on others in the meantime.
Yep. This. Those "lot of people" that still love their "first loves" need to figure out what they are really feeling. I still have a fondness for a "first love" but I wouldn't say that I still love him. I was friends with his wife for a while until he said that he was a little uncomfortable because he still had feelings for me. Instead of determining what those feelings were, or meant, I backed off. He had mentioned it to her before they both told me and I am the one that volunteered to leave the situation. She was a fantastic friend and I'm sorry that we've been reduced to mere acquaintances but I didn't want to be "that girl".
When you truly love another person, you don't love someone else in the same way. There's a lust, nostalgia, fondness, etc. But not love.
He should also, under no circumstances, be involving her by venting to her after every fight. He is sabotaging his marriage because there is either something with this other woman that he thinks is blossoming (or already has) or he is generally unhappy. I am so sorry this is happening to you (but to see it from both sides) I don't think there is much to salvage here. If he won't stop, he'll lie about it. Attempt counseling if you must, but I don't think you'll find the answers (or results) you want.