I am very sorry that you are in this situation. I agree with you that he has to be honest about his emotional affair and has to be willing to break it off completely with her, if your marriage stands even a chance. Just make sure that:
1. if he does that, you will be able to trust him again. Because as you know no relationship can work without trust.
2. he also wants your marriage to work. There's no point getting into the ring if you are the only one fighting.
I truly wish you the very best and hope you two can work things out.