Trying to build an animated swiss cheese infographic

That graphic would probably be simple to do in a 3D program, but as Rick already explained in AE you have to do quite a bit of extra masking to create the illusion.

Mylenium

Masking is the first screenshot, and 3D layers have been used in the second. You will have to make the layers 3D or add masks or a track matte to the horizontal line. Here are a couple of simple examples.