What's the chances of someone being discharged from the military if they commit adultry?

Slim at this point. They didn't remove a president for it and he was the commander and chief.

It is still against the rules and it is possible, much more likely to receive another form of disipline.

Im going to chime in here and say virtually none, unless the person he cheated with happened to be the Company Commander's wife.

Sorry - it might be a law in military, but I assure you - no one cares. Just file for divorce and move on.