Either way - at least one of them is upset.
This case, the husband is asking - so I gave a suggestion for how the husband can approach the situation. If the wife were asking I would give at least a similar response.
Instead I will change the wording so it is not anything to do with man or woman (so can be used in same-sex marriages as well).
Your spouse appears unhappy - your spouse is speaking with someone else becauase they need someone to listen to them. Maybe you should speak with your spouse and see why they are unhappy and how you can work together to make things right.
My suggestion wasn't such as one person is right or wrong - my suggestion was such that to start a conversation to work on their marriage.
If this were happening to me, I would talk with my husband and ask why are you unhappy I thought we were happy (assuming I was happy) - what is going on? And then try to work on it - both of us. I think I was taking the approach that the wife was talking with this man because she wanted someone to listen to her not to sleep with. If this were the case, I'd be pissed he didn't talk with me about being unhappy first, which I would know if roles were reversed he would be damn pissed I didn't speak with him first too. But then after initially getting angry we would talk it out - it depends on how much you value your marriage and how much you care about your spouse.
You are also assuming the woman is cheating - she said she wasn't. There is no way to know for sure unless husband saw them together. Simply talking with someone that is listening is not cheating -
I certainly do not condone cheating among couples - but we don't know if she is.
I guess the question for the husband is - do you trust your wife? Do you think she would lie? The husband would know more than us.
If she were cheating, would you still want to work on your marriage? Are you more concerned about the potential cheating or on you together as a couple?