Depressions are topographic areas that have no outward flow and occur in portions of landscapes with little to no elevation change, or areas with negative relief in relation to surrounding areas. While these depressions are an important part of the hydrological system, they have historically been filled in or ignored during flow routing and other hydrological processing calculations. With the increased prevalence of high-resolution topography data, understanding and evaluating how topographic depressions can impact overland flow is vital for improving hydrological analyses, specifically in the context of flood inundation mapping. Flooding caused from the filling of depressions (pluvial flooding) can have compounding effects when simultaneously occurring with river (fluvial) or coastal flooding. Our goal is to consider both pluvial and fluvial flooding in flat urban environments to identify areas that are significantly more vulnerable to inundation as compared to flood mapping from only one particular source. Our approach relies on a multiplex network that utilizes the Height Above Nearest Drainage (HAND) method as well as a hydraulic head equalization algorithm to estimate inundation patterns. Social vulnerability data are integrated in this framework to identify urban hot spots, defined as areas with a lower relative socioeconomic status in conjunction with a higher probability of inundation. Combining technical and social information leads to the identification of communities that are more vulnerable to the physical, economical, and social components of floods. This approach can help urban flood planners associate social disparities in relationship to flood preparedness and response.