OP, I'm sorry to hear that you are going through these rough times and that your husband has been dishonest with you. It know it must be very hurtful.
I think this is some good advice from Iister Laayla, albeit hard to do because our ego gets in the way, but I think you should try to heed this advice sister. But I would add to that that you should talk to him about making that relationship halal. Clearly he doesn't want to cut her out of his life, so the only option is to marry her permanently or temporarily. So advise this for him so that he doesn't keep doing haram. And unlike what one of the other posters said above, it doesn't mean he doesn't love you or care for you, but it means he cares for you and her. It's not worth it to keep fighting over this issue, you have to move forward. And maybe it's just short term infatuation, maybe if both stop talking about it and focus on YOUR relationship, he will get bored with her and call it quits on his own terms. But you can't control him, you can only control yourself and try to turn these lemons into lemonade as they say.
However you choose to deal with it I hope for peace and happiness in your marriage.