You may select both/all paths and Object>Compound Path>Make, and then use the Compound Path as the Clipping Mask.
If you tire of accidentally selecting the outlying hidden parts, you may, with the Mask selected:
1) In the Transparency palette/panel dropdown select Multiply (or anything else other than normal);
2) Object>Flatten Transparency (just leave the default 100% vector in the balance).
This will leave you without selectable outlying parts outside the Bounding Box; it may also destroy some vector artwork by outlining strokes, but leaves raster images unharmed.
Some may post here to say that all this is silly and should be different.
Draw all the shapes you want to use for your mask. Then, select all of
them and subtract the inner shapes from the outer shape using the
pathfinder palette. Now you should be able to select your clipping shape
and the item to be clipped and make your clipping mask.
Now you have two suggested ways of creating a Compound Path/Shape (the latter may be the result of the latter suggestion, depending on version, and be irreversible beyond Undoing, or should I say irreleasable).
It should behave just like any other basic clipping path. Why do you say
it is irreversible or irreleasable?
At least in some earlier versions, such as 10, you have to take precautions (pressing Alt in 10) to avoid ending with a Compound Shape that cannot be released, as can a Compound Shape. So if you wish to change a Compound Shape governing the Clipping Mask, after you have run out of Undo options, there is no way back. It is nicer to hear than to see.
I never assume anything about the version used by the OP, and in any case it is often a good thing to cover the different versions for the benefit of other readers.
It wouldn't still be possible to direct select and edit/move/delete only
the interior shapes? My memory is a little fuzzy on the limitations of AI
10 and previous. I know my method is sound for version CS through CS4
That will be possible, but you ill be stuck with a Compound Shape even if you delete everything but one path.