Is there a term for "inner circumference"?
Only on circular objects.
Otherwise, it is an "internal perimeter" which, as we will see, is a useless measurement.
Assume a box of exterior dimensions 20cm height, 41cm width and 32cm depth that has, for example, internal dimensions of 19cm height, 40cm width and 30cm depth.
three external perimeters = 2(width + height) = 122cm; 2(height + depth) = 104cm , and 2(width + depth) = 146cm and
three internal perimeters = 2(width + height) = 118cm; 2(height + depth) = 100cm, and 2(width + depth) = 142cm.
You will now note that of the 6 perimeters, no two are the same.
You will also note that, for a general box, it is uncertain which side is the top, bottom, or side
For these reason, there is no easy solution to your description.
The effect of this is that as a general concept what you are asking must be described as a clause.
Even in a specific case, where the orientation of the box is known, it may be possible to describe the internal and external (width + depth) measurement as “the horizontal perimeter” but this leaves the two dimensions that include height as undescribed and indescribable in a short phrase.
Out of interest, do you have specific terms in your language?