A wormhole might be possible, but an unlikely explanation of a black hole.
If you take the classic definition of a black hole being a super dense mass surrounded by an event horizon. The question would be the density of the matter within the black hole. Some theories indicate a point singularity, but that may be too great of a density. It is likely that no type of atmosphere could exist within the event horizon, as gravity stopping light would surely crush any particles containing mass onto the central body.
So, the maximum depth would be half the diameter, or the radius of the event horizon. Depending on the volume of the central body, it could be a lot less.
Do we need some kind of odd contracting space as part of the calculations too?