I have been through this and my marriage lasted another 4 years after the first affair (that I knew of). He did it again and thats when I decided enough was enough. He did beg and plead with me to give him another chance but during those 4 years I guess I had strengthened myself and was ready to be on my own. My kids were 12 and 15 at the time and my biggest regret is that at their ages the whole thing was very very painful for them.
My ex did not do much to try and change and he wouldn't let me talk about the affair, he just used to get angry when I got angry or upset. When I made my mind up there was no changing it - he did beg, plead, cry, rant, rave, threaten etc to no avail.
If your husband is prepared to let you get it all out of your system at him, including your very natural anger then you probably have more of a chance of surviving this. Even now after 5 years my guess is that you still feel angry now and then and also hurt.
Best of luck.