Rigging Arms Composed of Several Layers

Before giving up on the software entirely, I thought I'd post my question here.

I've done a lot of animating in After Effects, and I would always have arms composed of several pieces - a shoulder / arm base, a forearm, and a hand. Each would be its own piece of art you would import separately. Those 3 pieces would be parent/child rigged together. This makes far, far better motion without amateruish-looking rubbery bending at the joint.

But I can't find any tutorials on how to rig such a traditional puppet in Character Animator. They all seem to start with the assumption that the arm is a single layer that will just bend using CA software tools (ug!). Could anyone direct me to a video or document that would show the process to rig a traditionally, professionally built puppet in Character Animator?

I'm going to have to abandon the software if it can't even do fundamental parent/child stuff, but if it's possible, I would really love to understand how.