Many people split up and I haven't seen a couple yet who hasn't either blamed each other. You have to be honest with yourself and take partial responsibility for the split-up because it takes two. It doesn't make you a bad person, and you are no more guiltier than he is because when we take marriage vows it's for a lifetime, but many never see the marriage right through.
Sit down and write a list of the good/bad about your marriage. On a separate page write down the things you don't like about him, and then be brutally honest with yourself and write down the things you could have done to help mend this marriage. Put the paper away for a few days to a week, then take it out and you'll see one huge pattern of where things went wrong.
If you think he's worth keeping, then put your pride aside and meet with your husband and ask if he thinks your marriage is worth saving or if he wants to remain with this woman. Sounds to me like he really wants to stay, but not in the capacity you have been both living in. He wants a change, but doesn't know how to go about it with the exception of another woman in his life and it's going to take both of you to try. He is blaming you because he also feels like a failure and by seeing another woman he is feeling very guilty. Believe it or not that's a good sign.
If he is persistent in staying with this woman, then grant him his divorce. Don't hang on to something that is not there. Be strong, and don't be fearful about the future because it will work out for you too. I have been divorced (my husband a womanizer and dishonest in other ways) and it hurt terribly when he would say miserable remarks to me, let me know he was cheating and get great pleasure in the pain he made me feel. Then he'd get angry and I knew he hated himself for it. Instead of hoping, wishing and wasting my life I kicked this guy to the curb and moved out. I was afraid, I felt like a failure in my marriage and I also felt like a complete idiot because my parents and good friends knew this guy wasn't right for me, but being young I thought I could change him. Well, I sure learned different! In 4 years I was introduced to my husband that I have been happily married to for 33 years. If you grant this divorce, then take this time to know what and who you are about and gain strength from the past mistakes instead of them driving you into a mire of guilt. We learn by our mistakes and there is no guilt in that.
There are no failures in marriage if you have tried your very best, but if your partner won't work things out there is no point in staying in a miserable marriage. It's then time to move on.
Good luck Marcy
Thank you very much for your answer. I read it initially, but I failed to respond. I'm rereading it now and I have to thank you.