This is an interesting thought experiment.
If you haven't yet, it might be informative to read this "Aircraft Carriers in Space" article from Foreign Policy - it's short and pretty interesting: http://www.foreignpolicy.com/article...pace?page=full
Here's an excerpt:
Science fiction authors and moviemakers tend to gravitate towards historical models they -- and their audience -- understand. So, sometimes you end up with "submarines in space" -- but a submarine is a vessel designed to hide under the water, which obscures your vision and forces you to use capricious sensors like sonar. Space, on the other hand, is wide open, and any ship putting out enough heat to keep its crew alive stands out from the background, if you have enough time to look. Other times we get "dreadnoughts in space," with gunnery duels like Jutland -- but again, hiding is hard, so this battle should take place at extreme range. Or you get "airplanes in space," which largely ignores that airplanes work in the real world because they take advantage of the fact that air and sea have different attributes.
All of these models are fun, and some work better than others, but they all present space combat in a way that doesn't really fit with the salient attributes of space. And lest I get a thousand emails from people who say I don't understand how combat in their favorite universe works -- yes, I do. My answers are necessarily approximations for this interview. Someday I should write a book.
Another thing to keep in mind is that divisions between military branches aren't tightly drawn. The Coast Guard actually predates the US Navy for example, and has had different, but complementary roles for most if its existence. (Actually, that might be an interesting model to look at for an orbital force, depending on what they do).
And although the Air Force is generally thought of as the branch with the planes, the Army, Navy, and Marines all have their own planes and pilots within their own branches. (Although this is perhaps not a given; in some countries, the Navy operates the aircraft carriers, but the airforce flies the planes on it.) So it's quite possible that while the Orbital Corps is the main space-based force, the Army, Navy, and Marines may have their own ships for their own purposes.
(And of course the Marines are interwoven with the Navy of course - the "corpsmen" who serve as medics for the Marines are actually Navy enlisted men (even in places like Afghanistan)).