Talk to him about it and see where that leaves you. My husband has had a couple "work wives" -- coworkers who happened to be women and with whom he worked very well. He's still in touch with one from a previous workplace. And I have a "hobby husband" -- a guy who runs in my hobby circles I've known for a very long time and who I have a great friendship with. Both my husband and I have run errands for these people, just as we would do with our same-gender social friends.

As long as no one is hiding anything and being upfront about their feelings, having a "work spouse" isn't an inherently bad thing. I imagine if there were actual cheating going on, the two of them would be trying harder to hide it at work instead of being so brazen.