when i import photoshop or character animator images with layers into illustrator the layers parent

If its a PSD file don't worry about it - I think it does that at times (I normally use Illustrator). But you will need to create a deeper hierarchy to represent the puppet structure. The nesting of groups is important to Character animator to work out how things related to each other. You might have a look at some of the sample puppets to see how they are normally structured (pick a simple puppet first, not Sticky!).

For example, you might have a group called +MyCharacter. Inside that put a "Head" group. Inside that draw the artwork for the face and add a "Mouth" group. Then all the different mouth expressions go under that (with the exact names of the mouth visemes). Then CH will know how to speak - because it looks for Head -> Mouth -> Visemes.