If you can speak the native langauge, one option is to look into an American based company that has a subsidiary or something that brings in revenue in that country. For example, I work in the hospitality industry. If the opportunity was there and I was qualified (speak the language, etc.), I can work anywhere in the world (provided there are no restrictions w/ regard to hiring American Citizens).
Being that you are in the military, maybe there is a company that does contract work for the Pentagon and other U.S. federal agencies/departments (e.g, Haliburton) doing business in that region.
What about Foriegn Service? Or working at a U.S. Embassy located in Asia?
What kind of work do you want to do? Is pay important? Have you looked on the career websites to see if jobs in Asia have been posted?