The Article of War, 1806 (found at a web site of the 91st Pennsylvania) does not mention homosexuality, nor sodomy, nor any type of "sexual crime." There are 101 articles in those Articles of War, and where they do not refer specifically to uniquely military concerns, simply refer to violations of the laws of the locality in which a military post is located. They applied to the army, the marine corps and the navy.
The Articles of War were not revised until the eve of the Great War, more than a century later--i've not been able to find a copy of that version of the Articles of War, but i assure that they do not refer to homosexuality, either. The Articles of War were replaced in 1951 by the Uniform Code of Military Justice.
As George points out, sexual relations among serving members of the armed forces at any time and under any circumstance can be antithetical to good discipline and order, and it is completely within reason to make such a policy. However, just as the Articles of War might once have punished "sodomy" because it would have violated the local laws, but that is no longer so--i consider it reasonable that even though policies might once prohibited homosexuals serving, the change in social attitudes mean that such policies should no longer exist.
Where troops are not serving in harm's way, nor at sea, there is no reason for their officers to inquire into their behavior when off duty. When members of the military
are at sea, or going in harm's way, sexual liaisons, whether hetero- or homosexual, are reasonably prohibited, as destructive of good order.
This clown Pace is probably a narrow-minded, right-wing putz--but so long as he preforms his duty as he is required to do, and does not actively challenge the policies which are imposed by his civilian masters, he has every right to hold the opinions he has expressed,
and to express them.
There have been some confused contentions made here--but the fact of the matter is that the "don't ask, don't tell" policy dates from the Clinton administration, and the Chiefs of Staff of the services do not determine such policy, but are simply required to assure that such policies are put into effect--whether or not they approve. If Pace felt that he could not in good conscience do so, he should resign. Those complaining here about Pace who cannot demonstrate that he is acting against the dictates of the policies of the civilian administration to which the military is subject, really need to get a grip and lighten up.