As a Staff Sergeant (E-6), I served in a “purple” (joint service) environment. Heck, it was technically a coalition operation, although I personally had no contact with foreign militaries.
I knew, in general terms, what the Air Force personnel I worked with did, largely because their desk was next to mine. They were technically seconded to the staff section I worked for, but operated almost entirely independently. If it came down to it, I’d have had no idea what to tell their enlisted members to do, other than, “Do what you normally do for the staff briefing.” Even at the general administrative level, I’d have had no real idea on what to do with them. I know they have different training requirements, pay and promotion policies, etc., but I wouldn’t know what they are or even where to look. I knew quite a bit about which Army Regulation or Field Manual to look in to answer questions about Army procedures, but I don’t even know the proper terms for Air Force equivalents.
I served with two Marines who were seconded to my staff section. For no apparent reason, the Special Security Officer billet, at a U.S. Army command, was specifically a USMC enlisted billet.:dubious: I could have supervised that position, since he wasn’t actually performing USMC-specific duties, but, again, I’d have had no idea about even pretty basic administrative / supervisory things (do Marines get NCOERs, for example?).
The other Marine was my supervisor for while - he served as my staff section’s Administrative NCOIC (Non-Commissioned Officer in Charge). That was an open billet - it got filled by personnel volunteering from other units, since the unit that ran the command wasn’t really staffed adequately for what it wound up doing (this was in 2005, when the U.S. Army started suffering a lot of recruiting and staffing issues). Anyway, as his subordinate, I had to give him a lot of on-the-job training about U.S. Army administrative policies and procedures, which was made even more fun by the fact that I wasn’t an admin specialist myself (again, staffing shortages), and only had OJT myself. It helped that he had served in joint commands before. So, at the level of Sergeant First Class / Gunnery Sergeant (E-7), for an admin post, there’s definitely some cross-compatibility, but if he had been on his own, he would have been pretty screwed.
There were also Navy and Coast Guard personnel, but I had only the vaguest idea of what they even did, and there’s no way I could have supervised any of them.