While you guys have great points, this is the international thread... not the USAjobs thread. The USAjobs site is really not a gateway to overseas DoD paramedic level jobs. They are almost all exclusively contracted or military personnel. While I see the implication on the surface, they are really not related. International DoD Computer engineer, maybe... International DoD Paramedic, nope. I know he mentioned it, but it is really a non-starter and that's a tangent that has (or should have) its own thread.
As for the OP... That is a very broad brush to paint your question with. DoD experiences vary vastly from Germany to Ohio to say, Afghanistan. Mostly though, the positions are all contract. I have no first hand experience working in Germany. You would probably do well to do some internet searches to see who the providers are at the bases around your prospective area. They may utilize their own folks, contract to locals, or they may contract to US companies such as CHS or one of the other hundred million. Although, I have been in and out of contracting overseas, and I have never seen a paramedic job in Germany. I imagine it would fill very, very quickly if it was even posted... by someone who has the juice to get into a spot like that.