How to fix "Jumping" Tweens when using Layer Parenting?

I'm creating an animated face involving numerous layers parented to each other. Each layer makes up the face, nose, mouth, eyes, pupils, .etc. All the drawings are Graphics and I want them to move all at once, so I create my keyframes and move each part of the face to the place that I desire, and apply a Classic Motion Tween to all the layers. It seems to work at first, but for some reason by the time it gets to the last keyframe, all the parts of the face "Jump" to the last keyframe. It's as if the Clasic Motion Tween didn't track the first and last Keyframes properly. So in the end, I have a face that transitions from its initial keyframe and then suddenly cuts to the final keyframe. It's really annoying and I want to know if anyone ever experienced this or if there is a way to find out why it's happening and how to prevent it from doing that. Thanks.