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

The spouse needs to know get the pain out the way. But if they stay together that's there choice.

tell the other spouse

Who is in the military? The cheater or the spouse? If the cheater is a civilian, there is really nothing at all that you can accomplish with this. If the cheater is in the military, there still is pretty much nothing short of a reprimand that can be done. My advice is to look at the situation, and if it is affecting your unit's mission or morale, then address it at the lowest level possible --assuming you are the supervisor. If you are just a peer, and it is your coworker, you have a judgement call to make. Do you tell the betrayed spouse? It isn't really any of your business unless it is effecting your mission. A lot of this is situational, and there isn't enough information here to make any kind of suggestion. But be wary of getting into other peoples' private matters, it can really backfire on you.

Contact the show "cheaters"

Well I introduced my ex-wife to her current husband a week after I finished reading “The Prince” by Niccolò Machiavelli. That is a true story, by the way. I have all been happy these many years after I told him take my wife please.

Don't involve yourself! In the end he will only end up believing her!

Good question. When I was deployed, my husband moved in his girlfriend who was an E5/SGT. She also was married. I went to my 1SG, CID, and Jag. No one would do anything. She was gone when I got home, but her mail still was coming to my house. She PCSed, so I kept sending her mail to her new 1SG. Still nothing was done. So I would be surprised if anything is done.

This is a sharp, 2 edged sword. What is your co-workers motivation to do something? If there is true justification such as being a family member, etc. then they probably would want to talk to the wife first of all. If the co-worker is not a family member but has an interest motivated by preventing harm to children for example, I would suggest contacting a member of the husband's chain of command or a clergymen/Chaplain. If neither of these scenarios apply, I would strongly suggest that 'they keep their noses out of business where it doesn't belong.

It's unwise to get involved in other people's relationship problems or try to give advise, so I don't. But I'm a female though. Don't guys have to follow Bro Code or something?

Consult the 1st Sergeant and Chaplain on this one....A LOT to consider here, you never have the full story in these situations.....especially if PTSD, mental illness, abuse, or addiction is involved.