If you need to breakdown the area by the internal and
external area I would recommend creating a quilt
(surface copy) of the inside or outside of the model to
measure area.
Typically the quickest way to do this would be to use
the "seed and boundary" selection method. The help menu
should be a good reference. First you select the "seed"
surface, a surface you want to include in the quilt,
then while holding the SHIFT key, select the boundary
surfaces (surfaces you do not want included) that define
the limits of your quilt.
You can visualize it as pouring water on the seed
surface, which spreads and covers all surfaces it
touches until it reaches the boundary surfaces (which
act as a dam).