Question on boundary integral for interface of a two-domain problem

I am using DG for a two-domain problem.
The domain is a small square inclosed in a large square.

The question is when I do symbolic integration
a += symbolicBFI(uv, VOL, skeleton=True)
does this skeleton integrator include the integration on the interface of the two domains?
It seems I can integrate on the interface boundary as follows:
a += symbolicBFI(u
v, skeleton=True, definedon=mesh.Boundaries(“interface_id”))

I am quite confused…