When using partially-opaque textures on any cube added to a model, faces behind that partially-opaque texture will be backface-culled as if they are fully-opaque. Fully transparent textures will work fine, but any partial transparency will cause unintentional culling when viewed from the right angle.

This issue is really easy to test, and I'll provide a model that does exactly what I described here. This might just be a problem with how Minecraft does its rendering and might be entirely infeasible to solve, but it's worth asking about here. Thanks in advance!

This's my backface testing rig. You can open it up in your own copy of CPM and wiggle it around; all of the partially-opaque pixels should look at least a little weird to you.
backface_tester.zip