Adultery - Jewish Law
My wife confessed to having an extramarital affair. What does Jewish law say about how to proceed?
The Aish Rabbi Replies:
If you believe her, then you must divorce her immediately. (Furthermore, she is prohibited from marrying the second guy, the paramour.)
However, you the husband do not have to believe her. You can doubt the veracity of the "confession," and thus do not have to divorce her.
In these matters, it is always best to consult with an authority in Jewish law to make sure you are doing the right thing.
As for your wife, if she believes that she had an extra-marital affair (regardless whether the husband believes her), she should privately repent and make a firm resolution never to repeat. She should certainly avoid further situation that may possibly lead to such a contact. (source: "Maimonides" Laws of Teshuva 2:2; Code of Jewish Law - EH 178:9; "Igrot Moshe" EH 1:24)