Fluviodeltaic systems commonly display a compound-clinoform geometry that consists of a subaerial/subaqueous delta couplet. The extent of subaqueous delta development varies significantly and, in modern systems, is a function of fluvial input and basin hydrodynamics. We present a model of fluviodeltaic progradation in which the repeated occurrence of characteristic terrestrial floods and large coastal storms drives fluvial and shallow marine morphodynamics, respectively. We couple fluvial and shallow marine sediment dynamics via the surf zone, which we collapse to a shock condition and treat as a moving boundary. With steady sediment supply and sea level and simple basin geometry, our model naturally develops prograding deltas with compound-clinoform geometries. The subaerial delta grows via fluvial aggradation and shoreface progradation, whereas the subaqueous delta expands through foreset progradation, with only minor topset aggradation. The interplay of fluvial input with the wave/current field controls the basic partitioning of sediment between subaerial and subaqueous deltas and, by extension, the compound-clinoform geometry. Increasing the frequency or magnitude of coastal storms, decreasing flood frequency or discharge, and reducing grain size all increase the fraction of sediment delivered to the shallow marine environment and the extent of subaqueous delta progradation relative to subaerial delta development. Our model, which emphasizes the intrinsic coupling of fluvial and shallow marine sediment dynamics and downplays the importance of allogenic fluctuations, can explain many of the first-order morphologic features of natural delta systems, including significant lateral separation of the shoreline and clinoform rollover and differing rates of subaerial and subaqueous delta progradation.