After 6 years here and currently at the worst point ever - separated and STBX openly with OM, I am hardly the person to give adivce!!!
But...I will tell you this. Either the affair ends or the job ends before you can reconcile. As long as the cheater is still working for the OP, there will always be pressure on the cheater and doubt in the mind of the cheated upon.
As recently as 3 months ago, I believe STBX was trying to quit her job and get away from OM in the process. But, she didn't and now she feels trapped. At least that's what I think.
In our case, he owns a restaurant that she manages, so there is no HR dept. But if they were employees at a large company and he was just her boss and not the owner, I would certainly be tempted to let HR know. But that probably isn't a great idea.