The Military is a gathering of all branches of a nation's defense. Two nations' military forces are present in the Mafia Series; The Italian Army and the United States Army. There are four branches of the U.S. Military: The U.S. Marine Corps, the U.S. Navy, the U.S. Army and the United States Army Air Forces.
Vito joined the military, or more specifically the U.S. Army and the 504th Parachute Infantry Regement of the 82nd Airborne Division, during World War Two, so he did not have to spend time in prison.
In Mafia II, different sorts of military is encountered in two chapters of the main game. In The Old Country, where the United States and Italian Armies are encountered, and in Home Sweet Home, where United States Army Air Forces are encountered as their planes are flying over Empire Bay.