if he said he wouldn't do it and if he is still with the same woman, i feel it is time for you to take a stand. this surely is no one time affair, but a relationship. so you need to ask him what is it that he wants? does he think he can continue with the marriage as if all is fine, and also continue a relationship with the other woman at the same time? lay down some ground rules and if he really is not ready to leave her, please take a call and move out. maybe you leaving for some time will give you both a better look at where your marriage stands and how you want to go ahead with it.
if he is still in a relationship with her then it means something is serious here. talk to him and ask him directly what he wants. if he is okay to cut off all ties with her then maybe it is fine, but if you are sure he can't then please think if you are okay to go on like this for life. also, it can be possible that in future he leaves you and wants to be with her only. then? maybe you guys can shift to a different city and start again?
this will totally be your call, since you already know that he is still continuing another relationship. i am no one to tell you what you should do here. you love him, he may be loves you and does love the other woman. now it is entirely up to you if you are prepared to share that love, as long as you feel he is giving you enough time and love as well.