I will describe joint work with Jared Wunsch on propagation of singularities for some semiclassical Schrodinger equations where the potential is not smooth in directions normal to an interface. Singularities of a given strength propagate across the interface, but only up to a threshold. This is due to diffracted singularities which are weaker than the incident singularity by a factor depending on the regularity of the potential. Applications will be given to logarithmic resonance-free regions and long-time asymptotics of quantum evolution.