I've already posted this tutorial on the Open Source Filmmaker forums, but I thought I could share I how I dealt with the problem of backface culling (aka that situation where your models are invisible from the inside) here on the Blender Tutorial forums. You just need to follow these steps:

1. Turn on backface culling in Blender by pressing N in the 3D view. In the menu that appears on the right, scroll down to Shading and check the box for backface culling
   
2. In object mode, duplicate your object by pressing Shift+D. Press escape to leave the duplicate object at the same position as the original object.
   
3. Keeping you duplicated object selected, change to edit mode.
   
4. On the left hand panel, click on Shading/UVs
   
5. Under Normals, click on the Flip direction button. The backface culling should disappear.
   
6. Combine your flipped duplicate object and the original object. Rename if neccesary.

Special thanks to Zappy for figuring this out.