Welcome here little sister...
It sounds like your WH has some deep issues to work through. If your marriage is to get better, he has to fix himself. It sounds like he may have a strongly addictive personality where he seeks to medicate the only way he knows how - through band-aid approaches to sooth his ego.
We all have the capacity to say "no", but I believe your WH may have never fully developed that ability to a level where he can mean it. His choices are bound by fear and confusion. A fear of and of not understanding himself and a fear of consequences indicated by his promise to do right. Confusion from not understanding his true emotional needs due to past issues and replacing them with an inflated value on sex.
He probably feels very guilty right now, but with something so longterm and noncommital I expect you may see a promise/failure cycle and find that he compartmentalizes and kees the affair separate from the marriage in his mind. You'll likely find yourself on a wild emotional roller coaster.
He probably does place a lot of value on the marriage itself as it provides the stability and normality that he needs. The issue revolves around the fact that he doesn't know how to have a truly emotionally intimate relationship with anyone (thus confuses it with gratification).
As I mentioned, he needs to take care of his issues if your marriage is to have a chance. It all depends on how deeply engrained these behaviours have become. One of the biggest obstacles is that he may be in denial with himself that he has a problem or minimizing it. You need to think about what your needs are, about what you won't tolerate, and about what you will do to remove yourself from a situation which grows too painful.
The best thing you can do is to make your expecations clear. When communicating with him, keep yourself cool, composed, and assured. Any attacking/defensiveness on your part he will likely personalise and seek another quick fix. Calm and assertive is the way. At the same time, I would focus on pointing out any issues you see with his behaviour - for example asking him how long he thinks the marriage will last if his behaviour continues.
Now, while you are trying to figure out whether or not you wish to stay in the marriage (based on what your WH gives you to work with), you may find the 180 in the Healing Library as useful tool to focus on your own needs. It is a mechanism for one to detach from a hurtful situation and take control back over their life. I also suggest consulting a lawyer to find out what your rights are, and to consult your doctor/counselor to ensure that you are at your best for what lies ahead. Focus on what you can do for yourself to be happy, get involved in your life, take care of yourself, and focus on the fact that one way or another you will make it.
This is an exceedingly difficult time and you will bounce all over emotionally. You've been tossed into a place you've never wanted to go. But, I can assure you that there is a way out and that you can redesign your life and your relationships. It's normal to feel confused and scared - that means that you are on the edge of something new. Have the faith in yourself and the courage to find it.
You're gonna be okay.