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The most revealing thing to me here is that only the man involved expects you to keep this secret from your husband. Hey, let's conduct a little thought experiment. A woman is friends with a man who knows she is married. He is unhappy with his life, and wants out of his marriage. He asks her to keep secrets from her husband, while telling her that she is his best friend. What are his possible motives? It reminds me of advice my father gave me about quitting a job: have a new one lined up first. Good advice in one case, immoral at best in the other. You should be very cautious and reserved about this man. He may well hurt you and your family (perhaps due only to his inability to see beyond his own pain) if you are not aware of the coming danger. Do not keep secrets from your husband. Do not meet him alone. Do not talk on the phone with him at night. Do not be the shoulder he cries on. It may seem cruel to distance yourself from him, but your primary responsibility is to your family and your husband. Try to view his situation not as suffering that makes you want to comfort him, but as a personal failing that makes him less attractive and interesting. View his flirting, attentiveness and neediness as stress-coping mechanisms where he uses you, not as attempts to "reach out". Maybe this seems too pre-feminist, but the truth is that men are mostly capable of platonic friendship with women only when we don't want or need more.
Tell this guy that he stepped over the line when he asked you to keep secrets from your husband, and that you can not be his support system. Then ask your husband to help keep you out of it.