It seems that FAA requirements for any particular aircraft revolve heavily around the aircraft's type certificate. Civil aircraft are broken up into several categories based on weight or passenger count, etc. But I did not see a section on military operations.
In the US, the military is not required to obtain FAA type certificates for their aircraft; the FAA is not the authority certifying a military-registered plane's airworthiness. They have the option of accepting an FAA type certificate (which they tend to do on aircraft based on civilian ones), but they run their own certification agencies for airworthiness, which are all that matters if the plane is in the military registration system. Here's an Air Force policy on the matter, here's a Lockheed powerpoint on the option to use FAA certification on commercial derivatives.