Military Dependent living in Korea

I am a military dependent living in Korea and would like to get a multiple entry Visa to China. I don't know the dates that I will travel yet. I am currently in the states (Texas) and want to know where to apply for a multiple entry Visa. If I wait to get it until I get back to Korea, I can only get a single entry Visa. I have both a tourist passport and an official passport. I understand that I can only get a Visa on my tourist passport.