I gather that if you are a civilian instructor, you are a CFI. If you have your civilian instrument rating, you are a CFII. If you also have your civilian multi-engine rating, you are an MEI.
I'm a milcomp guy also, and I put those on my app as described. I think it's pretty easy to explain and justify it, but I'm not sure that it will even come up as they will look up your airman certificates and get copies before the interview anyway.
https://en.wikipedia.org/wiki/Flight_instructor