Hi, I'd like to help you with your problem.
It sounds like from what you said that your husband has a history of cheating in your marriage and when you confront him, he refuses to acknowledge your feelings and is not interested in working on the problem.
First, it is obvious that he has issues with staying faithful in the marriage. He is actively going outside the marriage and seeking out others. He is not being truthful with you. Additionally, when you find out about what he is doing and talk with him, he is not accepting responsibility and stopping the behavior. He appears uninterested in working on the marriage.
From what you said, this appears to be a problem with him. If it was an issue with your marriage, he would have been willing to talk with you about it and also work on it when you offered. Since he was not willing to do anything about working on it with you, that leaves the conclusion that he is unwilling to see this as his problem.
Since he is unwilling to seek help with you about this, I highly suggest you go to counseling without him. You need the support and someone to talk with to work out how you feel you would like to respond to what your husband is doing. You need to decide whether or not you want to stay in this marriage. Since your husband is unwilling at this point to take responsibility for his actions, it is unlikely he is going to stop the behavior. Is this something you are willing to live with? A counselor can help you decide what you want to do.
Also, if you and your husband are still having sexual contact, I recommend you see your doctor to be screened for sexually transmitted diseases. The symptoms of some of these diseases can be dormant and you can be unaware of them.
There are also books than can help you work out your feelings about what is happening. One is called Warning Signs: How to Know if Your Partner Is Cheating-and What to Do About It by Anthony DeLorenzo, Dawn Ricci, Ken Baron, and Frank Gunzburg Ph.D. Another is 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. These are available on Amazon.com or your local library may be able to get them for you.
Keep in mind that you are not to blame for your husband's behavior. Affairs are never the answer to marital problems and is always about the cheating partner, not the other person. You must focus on yourself and getting out of the situation and making your life better.
I hope this has helped,