Shallow water flow often evokes active sediment transport and changes in bed elevation and composition, which in turn conspire to modify the flow. The interactive processes of water flow, sediment transport and bed evolution constitute a hierarchy of physical problems of significant interest in a spectrum of engineering and scientific subjects. Depth-averaged shallow water hydro-sediment-morphodynamic (SHSM) models have been developed and widely applied to enhance the understanding of such processes over the last several decades. However, shallow flows can be sharply stratified under certain circumstances, comprising a clear water flow layer and an underlying water-sediment mixture flow layer, which depth-averaged SHSM models are unable to resolve. Here a double layer-averaged SHSM model for such flows is addressed, including the formulations and numerical algorithms. Typical applications of the model are presented, including floods due to landslide dam failure, turbidity currents in reservoirs, and landslide-generated waves in a reservoir.