A DHC is what it says. A coupe is a regular car (no half doors or side screens) usually a 2 seater and with two doors, and often with a lowered roof to the rear (coupe=to cut, ie seats and/or roof). A DHC is the same thing, but convertible (drophead).
A three position drophead can be entirely closed, open above the front seats, or entirely open.
Many of the body style names, coupe among them, derive from carriages. There used to be many more in use--when was the last time you saw a Salamanca motoring around?
A fixed pram hood = a faux coupe.
