The coincidence of fluvial and coastal flooding can lead to compound floods with substantial impacts on human life, property, and infrastructure. Low-lying coastal areas are particularly vulnerable to compound flooding because of exposure to multiple drivers such as extreme coastal high tides, storm surge, and fluvial flooding. In this study, we develop a bivariate non-stationary flood risk assessment that accounts for compound flooding from fluvial and coastal events with consideration of impacts of sea level rise (SLR). Extreme river discharge values were identified using peak over threshold method and were paired with the corresponding highest sea-water level within ±1 days of these events across the coastal contiguous United States. The statistical dependence between the paired data was assessed using Kendall’s rank correlation coefficient. For the locations with significant dependence, the best copula fit was used for bivariate dependence analysis by assuming non-stationarity in the marginal distribution of sea-water level data. The mixture Normal-Generalized Pareto Distribution model with SLR as the covariate is used to incorporate the non-stationary coastal flood frequency. The future risk was assessed using the notation of failure probability, which refers to the probability of occurrence of at least one major coastal flooding (i.e., water level exceed the major coastal flood threshold) or 100-year fluvial flood for a given design life. Failure probability was formulated to allow for changing exceeding probabilities over time. The results indicate that the joint exceedance probability of fluvial or coastal flooding can be higher when the dependence is considered. Ignoring the compounding effects may inappropriately underestimate the flood probability at locations that flood hazard can be influenced by the interaction of fluvial and coastal events. Moreover, with rising sea levels, the probability of exceedances of sea-water level over the flood threshold increases and consequently the compound flood probability increases as well. In the locations with less dependency between extreme river discharge and sea-water level, the frequency amplification of fluvial and major coastal flood events is higher.