If the man and wife had been communicating via snail mail, and the wife had hidden the letters in a little box with a key, but left the box and key lying around, would the husband have been trespassing if he used the key to access the letters? Doesn't the law consider all matrimonial property to be joint property? If it is acquired during the marriage, it is jointly owned.
I think it's crappy that the wife had an affair, crappy that she hid it, crappy that the husband had to do whatever was in his means to figure out why his life was feeling screwed up, and in a way, it's really good that the husband finally had the facts and was able to make good decisions for himself without being lied to and manipulated by his wife. Bottom line, it's all crappy, but I don't think the husband should have legal problems because he accessed joint matrimonial property to protect himself from being screwed over by his wife.