The OP is not asking about standard training to get a regular CFL. I'm MS you do not need to take a class to get you license. You have to fill out and notarize the paperwork, turn it in, pay your money, and wait. You'll be run through the FBI database and the local sheriff gets a copy of the app to check for warrants also.
We have an extra endorsement called a "Enhanced Carry" endorsement. You have to take a safety class approved by the DPS of MS and you are given a sticker on the back of your CFL. This is only valid for MS residents.
This endorsement allows you by law to carry in any normal place listed off limits to regular license holders with the explicit exception of jails, police stations, court rooms in session, and "places of nuisance" which in MS are defined as places where illicit gambling, drug use, prostitution and such are happening.
I'm honestly not sure what the military training you mentioned involves but I don't think it counts toward the enhanced. You can look on the DPS website at the list if enhanced instructors and ask any of them about that in particular.