Your description sounds like you didn't create individual layers in Illustrator. You need to do that.
You probably only have a Layer 1 in your Illustrator document. You need to create Layers 2-7, move the appropriate things into each layer, and it's also good to rename each layer with something that makes sense. Hard-core Illustrator artists blow that off right away. In the case of a human body, they would be Right Eye, aLeft Eye, Head, Torso, Right Arm, Left Arm, Right Leg, Left Leg. Just double-click on the current layer name and re-name away.