I have a coworker with direct knowledge of a Military spouse cheating on her husband. What action, if any, should he take?

They should be told, no matters what the circumstances because you would want to know if the ball was in the other hand.

I can only respond if I was in their shoes. If the spouse was my spouse, I would ask her up forward. If she denies (and the direct knowledge is verified), then I would probe her with questions about it. They can try and speak with a Chaplain, or engage in some type of assistance to help with anything that is not going well in their relationship.

If the co-worker is just a friend of the spouse, then I would just say "Hey, you know what you are doing is not right, right?" and then go from there.

If the SM is aware of the spouse engaging in extra-marital actions, then it's not my place to say anything. It maybe wrong, but it's not my relationship and I don't know their business.

But like I said, I can only respond if I was the person in their shoes. They may handle things differently than I would.

Report it to his first sergeant