Heightfield

It's really simple. No plain heightmap will allow you to do this. Not without some serious hair pulling at least.


I've been somewhat successful with some selective rendering to allow drilling holes (similar in concept to this) in the terrain and a set of cooperating terrain system. It would work... with some care, as edges shared across different terrain systems would be usually garbled. In the long run, the system didn't really convinced me. Perhaps some geometry shader tricks might help it, I cannot tell.
I general, I'd say voxel isosurface extraction methods appear to be more robust for that kind of application. I'd absolutely look at Eric Lenglyel's Transvoxel Algorithm.