In Islam when there is evidence that a husband or a wife has slept with someone else, he or she has to be stoned to death. That is allowed. The rules are strict of course, there has to be real proof that he or she did that.
So that means, a husband or even a wife can hit/kill the spouse if he/she is cheating on him/her. But there has to be evidence.
(Of course you can't help it when you do like someone else, it's a feeling Allah gives you to test you. You can like someone else, maybe even love someone else in your heart, but as long as you don't do anything with that feeling, just leave it as it is, it's oké and ask Allah to help you to deal with it.
Or if you still really want to be with that other person instead of your spouse, then first you should tell your spouse about it, first divorce and then be with that other person.)
But a husband should never hit his wife for any other reasons. People say they are following Islam even when they hit their wives, but they forget the ayat where it's written that they should treat their wives kindly.