The WebView is displayed as a native UI component and sits outside the display list and Stage3D content.
Native UI components are placed above the AIR stage and run as a separate component to your AIR content. This means that you cannot layer AIR content over a native component.
You can communicate to the WebView through the ANE using JS, AS3 events, etc.
If you require to animate the WebView and layer AIR content over you can use the 'screenshot' functionality to capture a BitmapData representation of the WebView. The BitmapData you can then use in your AIR content as a way to animate the WebView. Obviously the WebView is not interactive when you are using a screenshot to animate though.
Hope this clears up your issue.