Short answer: The military can't punish your husband for your relationship with your boyfriend. The UCMJ only applies to the active duty member... in some overseas locations there may be additional rules that you will have to follow as a spouse: such as curfews or dress codes.
Your spouse on the other hand could get into a bit of trouble for what the military considers 'adultery' but it is a bit complicated. The article which governs adultery is long and a bit convoluted but Google 'UCMJ Article 134' - http://usmilitary.about.com/od/punit.../a/mcm1342.htm
The three elements under Article 134 which must be present are:
(1) That the accused wrongfully had sexual intercourse with a certain person;
(2) That, at the time, the accused or the other person was married to someone else; and
(3) That, under the circumstances, the conduct of the accused was to the prejudice of good order and discipline in the armed forces or was of a nature to bring discredit upon the armed forces.
As far as punishments go I've heard of Commanding Officer's doing any one or combination of the following: forcing the active duty spouse to confess his/her crimes to his/her spouse, restriction (similar to house arrest-the service member is confined to a special barracks and only allowed to go to work, the galley, and the gym), reduction in rate/rank, loss of pay, reassignment to a different command, and/or discharge from active duty service (either by retirement or discharge).
I've not heard of anyone getting the maximum punishments of Dishonorable discharge, forfeiture of all pay and allowances, and confinement for 1 year. I'm a USN Veteran with 4 years service, married to a military man, and lived in a military community for the last 20 years so I've seen and heard a bit.
My advice, if he chooses to find a GF or BF of his own be sure that it is someone that if he weren't married he could be in a relationship with. IOW someone not in his command or Chain of Command, and within his own ranks (if he's an officer-only date officers, if he's enlisted-only date enlisted, etc..). Also, close ranks, so to speak. Keep all of your relationships on a need-to-know basis. And have a plan just in case his Commanding Officer does call you. Our plan was to be honest, forthright and to act surprised that poly is not something that everyone does.