Given where debris has fallen and where eyewitnesses were located when the accident happened, it appears the aircraft were outside of Charleston's Class D airspace in an area not far from Berkeley County Airport, KMKS when they collided.
A Shaw AFB spokesman has already said the F-16 pilot was on an IFR training flight and was talking to ATC. The F-16 was most likely on vectors or on an instrument approach.
At my last base (McGuire), this was one of if not the top safety issues noted each year I was there (being on an approach outside of Class C or D airspace and a civilian aircraft flies through the approach procedure).