Compound flooding is a type of flood event caused by multiple flood drivers. The associated risk has usually been assessed using statistics-based analyses or hydrodynamics-based numerical models. This study proposes a compound flood (CF) risk assessment (CFRA) framework for coastal regions in the contiguous United States (CONUS). In this framework, a large-scale river model is coupled with a global ocean reanalysis dataset to (a) evaluate the CF exposure related to the coastal backwater effects on river basins, and (b) generate spatially distributed data for analyzing the CF hazard using a bivariate statistical model of river discharge and storm surge. The two kinds of risk are also combined to achieve a holistic understanding of the continental-scale CF risk. The estimated CF risk shows remarkable inter- and intra-basin variabilities along the CONUS coast with more variabilities in the CF hazard over the US west and Gulf coastal basins. Different risk assessment methods present significantly different patterns in a few key regions such as the San Francisco Bay area, the lower Mississippi River, and Puget Sound. Our results highlight the need to weigh different CF risk measures and avoid using single statistics-based or hydrodynamics-based CFRAs. Uncertainty sources in these CFRAs include the use of gauge observations, which cannot account for the flow physics or resolve the spatial variability of risks, and underestimations of the flood extremes and the dependence of CF drivers in large-scale models, highlighting the importance of understanding the CF risks for developing a more robust CFRA.