Someone serving or, at least, not too old, help me out please. The correct terminology was:
"¢ Joint = two or more services, which led to e.g. the Joint Chiefs of Staff and the Joint Staff in the USA; but
"¢ Combined = two or more countries, which led to e.g. the Combined Chiefs of Staff (UK + US) in WWII and explains why we still have, today, the Combined Communications Electronics Board - see: http://www.dtic.mil/jcs/j6/cceb/ which appears to be a hardy survivor of WWII.
To address civvy3840's specific question: the answer is 'Yes' - sometimes, UN or alliance (NATO) operations, but, other times - as in the Gulf, with a coalition, or as part of US formations.