The pointer you have with asIScriptObject is the pointer to actual object. :) asIScriptObject is the public interface to the internal asCScriptObject implementation. An asIScriptObject can only be used for script classes. For registered classes you should use the actual C++ class to represent the object.

C++ interfaces should be registered to AngelScript just like an ordinary reference counted C++ class (RegisterInterface is for script interfaces, not C++ interfaces), and then you'll likely want to add implicit and explicit reference cast behaviours to allow casting handles between the various types that have any relation you wish to expose to the scripts.

You'll want to check out this article in the manual:

Class hierarchies