  Interest for spacetime structures has recently been revived, following
developments in metamaterials and ultrafast optics. Such structures essentially
consist of successions of space-time interfaces for which the theory is still
incomplete, in particular in the regime where the interface velocity lies
between the wave velocities in the two media involved. This paper addresses
this `interluminal' regime, providing exact scattering solutions for both
approaching and receding interfaces. The solutions are verified to be
consistent with the transmission matrix perspective and to be continuous at the
limits of the subluminal and superluminal regimes.
