Compound flooding, characterized by the co-occurrence of multiple flood mechanisms, is a major threat to coastlines across the globe. Tropical cyclones (TCs) are responsible for many compound floods due to their storm surge and intense rainfall. Previous efforts to quantify compound flood hazard have typically adopted statistical approaches that may be unable to fully capture spatio-temporal dynamics between rainfall-runoff and storm surge, which ultimately impact total water levels. In contrast, we pose a physics-driven approach that utilizes a large set of realistic TC events and a simplified physics-based rainfall model and simulates each event within a hydrodynamic model framework. We apply our approach to investigate TC flooding in the Cape Fear River, NC. We find TC approach angle, forward speed, and intensity are relevant for compound flood potential, but rainfall rate and time lag between the centroid of rainfall and peak storm tide are the strongest predictors of compounding magnitude. Neglecting rainfall underestimates 100-year flood depths across 28% of the floodplain, and taking the maximum of each hazard modeled separately still underestimates 16% of the floodplain. We find the main stem of the river is surge-dominated, upstream portions of small streams and pluvial areas are rainfall dominated, but midstream portions of streams are compounding zones, and areas close to the coastline are surge dominated for lower return periods but compounding zones for high return periods (100 years). Our method links joint rainfall-surge occurrence to actual flood impacts and demonstrates how compound flooding is distributed across coastal catchments. Plain Language Summary Compound flooding can result when multiple sources of flooding (such as storm surges at the coast and inland rainfall) overlap in space or time and interact in such a way that overall flooding is exacerbated. Tropical cyclones (TCs) often produce both storm surges and intense rainfall, and have caused many observed compound floods. We analyze compound flooding from TCs by using a large set of realistic TC events and a suite of physics-based models that estimate TC rainfall, storm tides, and simulate their interaction in a coastal study area (Cape Fear River, NC). We find that compound flooding is more severe during TCs that produce high-intensity rainfall and when significant rainfall occurs near the time of peak ocean water level. It is crucial to incorporate rainfall in coastal flood hazard assessment, and we find that neglecting rainfall results in an underestimation of extreme water levels in the study area. It is also necessary to model rainfall and storm surges together within physics-based models to accurately represent their interaction and compounding during TC events.