Basically me and my friend are looking for a co-op game that has missions like spec ops in mw2 and mw3, we loved completing them. We have played SWAT 4 already, it was somewhat similar, but we want more. We don't really care, as long as it has kinda short missions, it's pretty hard to explain but the spec ops missions are a good example. It doesn't have to be first person as long as it is a shooter.
Ah! The Spec Ops missions in MW2 were amazing fun.
Unfortunately, precious few games have been designed with similar elements; at least not military style games. The nearest one that I can think of off the top of my head is "Army of Two" which received mediocre reviews. If you don't mind stepping outside of the military-style paradigm, give Borderlands 2 a try.