Hi, I'd like to help you with your question.
It sounds like your husband is not respecting you or your marriage and is continuing this relationship despite the fact that you know about it and are being hurt by it.
You have a few choices here. Besides insisting that he stop the affair immediately, you need to have him to go to therapy with you. He needs to understand that having an affair, emotional or otherwise, is a good way to end your marriage. You can find a therapist by asking your doctor for a referral or if you attend church, your pastor can help you. Pastors are often very good at marital therapy. You can also search on line at http://therapists.psychologytoday.com/rms/.
Depending on whether or not your husband is willing to stop his behavior, you may want to try a trial separation. Sometimes, the space helps couples take time to work through issues without the added stress of arguments or poor interactions.
Either way you decide to handle this, you deserve the respect of your husband and you have the right to be able to trust him in what he says and does. If he is willing to work on your marriage, he will have to earn back your trust.
Some books that can help you decide what to do include Getting Past the Affair: A Program to Help You Cope, Heal, and Move On -- Together or Apart by Douglas K. Snyder PhD, Donald H. Baucom PhD, and Kristina Coop Gordon PhD and My Husband's Affair Became the Best Thing That Ever Happened to Me by Anne Bercht. You can find these on Amazon.com or your local library may have them available.
I hope this has helped you,Kate
You can refuse to accept that he is "friends" with this person. As long as you say you do not believe it, then he can say it all he wants and both of you know it is not true.
You can also stand your ground about what you want to happen. You have to decide what you want in your marriage and what you want your husband to abide by. If it is unacceptable for him to cheat, then tell him that. Then insist on therapy. Also insist on no contact with this other person. If he is not truthful about it, you will find out. Just like you did this time. Then you will have to decide the consequences- stay or divorce.
You will know if the marriage is going to work by how he reacts to fixing this problem.