I was actually faced with this situation. I caught my girlfriend's husband in their house with a young woman whom they had befriended and given her a place to stay.
My girlfriend was at work and her husband was off that day. I went by their house to drop off the serving trays that I borrowed from her for a party I had the weekend before. His car was in the driveway, and the other woman's car, which I didn't find that suspicious because she used to live with them, BUT it was in the middle of the day and my girlfriend was at work.
I knocked, but no answer. I kept knocking, but no one came to the door. I started calling his name, her name, saying to them that I know you're in there, open this goddamn door right now. He finally opened the door, acting nervous, and the hallway door leading to the bedrooms was shut. He first lied that she wasn't even in the house. He explained that she had dropped her car for him to take a look at. When that lie fell apart, he tried to deny that anything was going on with them. But the other woman, whom I had grown to know and care about, came right out and admitted the affair to me.
I was really hurt that they could do that to my girlfriend and torn about telling her something that would devastate her and mean the possible breakup of a 24-year old marriage. I went home and contemplated what I was going to do. Then it dawned on me, it was not my responsibility to tell her...it was his.
I called him up and told him that he had until one hour after she got off work to tell her that he was having an affair or I would tell her myself.
When she called me to tell me what had happened, I admitted to her that I already knew. I explained to her how I had caught them the day before and what I had told her husband. He not disclosed to her that I had found them together. He lied to her that the affair happened a year earlier but it was now over.
She thanked me for putting the responsibility back on him, but added that if I had not told her I had caught them together, she would have held it against me for knowing something like that and not telling her.
So, my answer would be to confront him and tell him to tell her or you will.