Same thing is happening to me. If I try to use the game's default custom heightmaps, such as Earth's, the continents will load fine. However, the heightmaps I had made for my custom race are now broken and result in totally blank planets -- though, interestingly, it doesn't result in Class 0 planets. The planets will still have their starting class set correctly, but you will be unable to terraform because there's no land. I have been gone a long time, since before 1.3, so somewhere in between then and now, custom heightmaps broke.
I even tried copying the Earth heightmap and just naming it something different, and even that caused the planet to draw a blank. Literally identical files, except for the name. Hilariously, if I rename my custom heightmap to the same as Earth's and remove the Earth heightmap from the Galactic Civilizations III\Gfx\planets\custom_heightmaps folder (which is where my custom heightmaps had been), the game doesn't seem to notice, and STILL loads the default Earth heightmap successfully, even though it is gone. It is as if the heightmaps all became hard-coded into the exe for some reason.
I'll try to get a bug report going in the morning.
Also I did delete these two directories and re-verified, because the 1.4 patch notes said to: