The service medals are the US Marines service medal and the RU service medal, both awarded for spending 100 hours in either service. As with the class service medals (Engineer, Medic, Recon, Support), only time spent as a foot soldier in-game counts. So any time spent in vehicles, aircraft, stationary weapons, does not count.
Note that time dead does not count towards your total play time, just like time in the menus. I can't confirm, but am led to believe this by seeing the BF3stats.com's reports (example). Note the round Duration (7:13 in the example) and the 'Time' field for the player (6:08 in the example). BF3stats.com pulls its data from the BF3 API, so I assume the reason that field is there is to calculate SPM.
I believe (but can't confirm) that time spent playing Squad Deathmatch counts as play time for the RU Army.