There is nothing wrong with mesh inflation at interfaces. In fact, the use of mesh inflation is always a good thing if by any chance the flow comes at a steep angle crossing the interface with large gradients across the interface.

Generally, mesh inflation is a technique to minimize numerical errors in areas where steep gradients exists normal to the surface. If you are certain the flow comes at a reasonable angle at the interface, and the gradients are gradual across it, you do not need inflation.

I perfectly agree with you in the general consideration...for this very case though, my personal approach would be with prism layers wrapped around the walls (crossing the interface).
Considered the position of the interface I'd probably spend some time trying to have conformal meshes across the interface (1:1 interface as called in CFX )