This sounds like an interesting application! What kind of project is this for? Is the goal to essentially be looking at the same satellite imagery...but as if the camera was in the center of the Earth?
There's currently a few assumptions in the engine that prevent underground rendering from working (such as the camera controller not allowing the camera to go underground, which you can disable. But also the renderer will cull objects completely underground since they are considered not visible, which is harder to work around). We are working on improving support for this generally but I don't have a specific timeline for it at the moment. There's some more discussion in this GitHub issue:
https://github.com/AnalyticalGraphicsInc/cesium/issues?utf8=%E2%9C%93&q=is%3Aissue+is%3Aopen+underground
You might have more luck creating an ellipsoid geometry and and texturing it. You'd need to enable backface culling to be able to see it from the inside, which might require working with a bit of the lower level primitive APIs.