Ummm . . . you are aware that the Earth and Moon also orbit a common center of gravity, yes? In that case, the center is actually inside of the Earth, but the principal is the same.
Yes... But Pluto and Charon's point with which they orbit is in mid space. I think that's an interesting distinction.
If the common center of gravity is inside the Earth, then technically the Earth doesn't "orbit" the center of gravity because a portion of the Earth is always on the other side of the center of gravity at one time or the other.
If you go with that distinction, Jupiter is not a planet orbiting the sun, either. Think about that, before you decide there is something spectacular about the central point not being inside the major body.
