•Trends in and dependence between sea level and precipitation increase the probability of compound flooding along US coastlines, most notably along the Southeast coast.•A Bayesian copula-based framework captures the uncertainty in the quantification of compound flood frequency.•Precipitation trends play a major role in increasing the uncertainty in compound flood frequency.•To account for non-stationarity, a long historical record is required. When elevated coastal water levels and heavy precipitation occur simultaneously or in succession, their joint impact may be exacerbated compared to their individual occurrence. Sea-level rise, shifts in precipitation patterns, and the presence of correlation between flooding drivers can increase the frequency of these compound events. In this study, a copula-based Bayesian framework that incorporates the impact of dependence between flooding drivers (i.e., sea level and precipitation) and accounts for the nonstationarity in these hydrologic variables is developed. The framework is used to assess how the individual and combined effects of dependence and nonstationarity influence the frequency and magnitude of compound coastal-pluvial flooding. Furthermore, the Bayesian framework allows for the incorporation of uncertainty, which may arise from shortage of data, model selection, and parameter estimation, into flood frequency analysis. The proposed framework is applied to 32 station pairs across the US coastlines to identify locations that experience the highest risk of compound flooding and to assess the major contributors to uncertainty in the bivariate return period. The results show that the Southeast Atlantic coast experiences the highest increase in the risk of compound flooding, followed by the Gulf and Northeast Atlantic coasts. Sea-level rise and dependence between flooding drivers have a larger influence on bivariate return periods than changes in precipitation patterns. Under a nonstationary framework, precipitation is the major contributor to uncertainty compared to sea level and dependence. In addition, results demonstrate that uncertainty is highly dependent on the length of joint data. This study highlights the importance of incorporating hydrological dependence and trends and associated uncertainty into the quantification of return periods to permit reliable estimation of flood hazards.