Adultery, while not a crime under the Uniform Code of Military Justice, would almost certainly be considered "conduct unbecoming" and it could be punished under this provision:

Though not specifically mentioned in this chapter, all disorders and neglects to the prejudice of good order and discipline in the armed forces, all conduct of a nature to bring discredit upon the armed forces, and crimes and offenses not capital, of which persons subject to this chapter may be guilty, shall be taken cognizance of by a general, special or summary court-martial, according to the nature and degree of the offense, and shall be punished at the discretion of that court.

Petraeus did the right thing as an officer, if he still is in the military.