Do you have a tendency for self-destructive behaviors? I'm just wondering because you were trying to repair your marriage after the emotional affair, and then had the physical affair.
Your wife feels like the only way to save the marriage is to revenge cheat, which means that no one in this relationship has any emotional maturity.
I'm with Annie, mostly. Are there children in this marriage? If there aren't, why are you wanting to save it? And if there are, you both need to get it together like yesterday, and get all kinds of counseling asap. Even if you don't stay together, your kids need some role models.
People can have affairs of any kind even if their needs are met. Some people do it just because they can. Please don't blame your cheating on your wife. If your needs weren't being met, there were ways to fix that before you went outside your marriage.