Amazing how many new usernames will come out of the woodwork with this thread.
Here is my take on the situation, and it is gleaned from conversations with other men and women who have had affairs, research on affairs and also personal experience. YMMV To the OP, yes, I think a man can love his wife, his children and his life and still have an extramarital affair. Is it easy? No. Is it honorable? No.
Does it happen? Yes, and a lot more than we think.
If we are truly talking about a man who IS happy in his marriage, gets along well with his spouse, may have many years of common interests and experiences to bond them together, then the answer usually does point to "because of sex". I think men very much can separate sex from love much easier than any woman can. (that is a separate debate in and of itself)
In most of these situations there is an incompatibility in the bedroom either with the frequency of sex or the type of sex. In a lot of situations where a "happily" married man has an affair, it is finding a new partner who is more adventurous and will do things his wife won't or he can't dream of talking to her about. The previous poster a page or so back mentioned that the mistress she encountered was a Domme, which tells me that the husband was interested in certain sexual fantasies that the wife probably was not, or he would not have gone looking for it on the outside of his marriage. This is not to debate the morality of his decision, only answering the original question of can a happily married man have an affair. It's the choice he has to make of either approach his wife with suggestions of what he wants and if he gets turned down, does he look for it elsewhere? Remember if you have poor impulse control and something you want is right there, it seems to be easy for a lot of men to compartmentalize an affair to the extent that the morals of it go out the window.
I also have had a friend who had an affair with a woman and fell in love with her; which shows that even if these men start off just seeking sex, sometimes that emotional connection is made, too. To my knowledge, the wife never found out and my friend remained in his marriage after the affair ran its course (these things rarely last forever). I think that if a man is looking for an affair with the love and emotional connection, too, that there is a very different dynamic in the marriage and something that is lacking emotionally for the man, not just sexually. So, if the OP has any details that would point to what kind of connection the husband has with the other woman, that may tell her a lot. Then the husband is probably not so "happy" as he looks on the outside.
A lot of men look at an affair as an escape, not necessarily from real life, but from reality for a short time. They separate the activity of the affair so effectively from their real life, that they truly don't feel as if they love the wife or children any less or are any less loyal to them because they never plan on leaving. Every affair has its own reasons, but it seems like the cake eaters just truly want "more". More sex, different sex, variety, fun, whatever. It usually doesn't have anything to do with any shortcomings in the wife.