Adcoms won't disregard your army experience - of course the majority of military applicants are officers who graduated from ROTC and the academies, so they may not see your army experience in exactly the same way, but the one advantage you have on them is your civilian experience - a lot of military applicants don't have full-time post-college experience outside the military (even though you don't have much civilian experience, something is better than nothing). If you're not working right now, hopefully you're keeping yourself productive somehow (other than writing the applications) -- either volunteer or organized extracurriculars that you may be doing in addition to job hunting. In any case, you're applying to a decent range of schools so you should be able to get into at least some of them.
Alex, thanks for your prompt reply. The "keeping myself busy" part is tricky. I plan to start my MBA in Fall 2010, which is about 1 year away. If I (by a long shot) get into the Wharton/Lauder program, it would start in May '09, which is even less time. This is not a lot of time to get a job that truly adds value to my resume.
Therefore, I accepted a scholarship to do some independent study in Beijing for a year, hopefully I can at least get some kind of internship/teacher's assistant position during the school year; I hope the adcoms don't see me as too "academic".