Sea level rise (SLR), a well-documented and urgent aspect of anthropogenic global warming, threatens population and assets located in low-lying coastal regions all around the world. Common flood hazard assessment practices typically account for one driver at a time (e.g., either fluvial flooding only or ocean flooding only), whereas coastal cities vulnerable to SLR are at risk for flooding from multiple drivers (e.g., extreme coastal high tide, storm surge, and river flow). Here, we propose a bivariate flood hazard assessment approach that accounts for compound flooding from river flow and coastal water level, and we show that a univariate approach may not appropriately characterize the flood hazard if there are compounding effects. Using copulas and bivariate dependence analysis, we also quantify the increases in failure probabilities for 2030 and 2050 caused by SLR under representative concentration pathways 4.5 and 8.5. Additionally, the increase in failure probability is shown to be strongly affected by compounding effects. The proposed failure probability method offers an innovative tool for assessing compounding flood hazards in a warming climate.