Hi, I'd like to help you with your question.
It sounds like your husband is excusing his behavior by putting the responsibility and blame on you. It is a way for him to avoid feeling guilty and responsible for what he is doing. He may also be in denial about his behavior and truly believe that you caused him to act out this way. Also, he could be narcissistic in which case he will see himself as more important than anyone else, including his family and the female he is seeing now.
Whenever someone cheats in a marriage, it is always their choice. No one can make anyone cheat. There are many options in dealing with marital problems, but cheating does not solve any issues. It only makes things worse.
Your husband is probably acting the way he is because there is something going on with him that needs resolved. He is either having a problem with the marriage and doesn't have the ability to address it directly, or he has an emotional issue that needs treatment. His inability to sign the papers for divorce shows that he is not sure what he wants. He may feel that having the safety of your marriage and your family is too frightening to him to give up. So he denies the outside relationship he is having so he can drag out the marriage with you. But he has difficulty handling being married and the issues that come with it so he isn't comfortable in the marriage either.
If you feel strongly about ending the marriage, talk with your attorney about your choices legally to get your husband to sign the papers. But if you feel you want to make a go of the marriage, then therapy is a good idea. You can either talk with your pastor if you attend church or search on line at http://therapists.psychologytoday.com/rms/. If your husband won't go, go yourself. You need support right now with this situation.
Either way, you need to decide what you want to accomplish and stick to it. It does not sound like your husband is sure of what he wants so it is, unfortunately, up to you. Making the choice will also help you feel more in control and you will be able to move forward with your life.
I hope this has helped,