Originally Posted by MI-Roger
My guess is a nominal 18-inches.
This is the same clearance between a standard height counter top and the lower edge of 30-inch wall cabinets when mounted below a 12-inch soffit in a room with 8-foot ceilings.
I don't know if this is the legal answer, but I doubt it: counter-tops generally don't have fire coming out of them.
Even if safety were not a concern, I would definitely want more space. My tallest pan is about eight inches tall, and 18 inches wouldn't leave much space for a spoon or ladle. The pan sits about an inch higher than the edge of the range, so there goes another inch. Also, anyone taller than five feet would have a hard time working at the stove with the microwave at that height.
The microwave right above the stove will get a lot of heat and a lot of grease. It will need frequent cleaning, which will be difficult if it is low.
My hood is about 22.5 inches above the body of the range and 21.5 above the burner grills (or whatever those things are called).
My preference is to use a regular hood, properly vented, and to put the microwave elsewhere.