Coastal watersheds are vulnerable to compound flooding associated with intense rainfall, storm surge, and high tide. Coastal compound flooding (CCF) simulation, in particular for low-gradient coastal watersheds, requires a tight-coupling procedure to represent nonlinear and complex flood processes and interconnectivity among multidimensional hydraulics and hydrologic models. This calls for the development of a fully-coupled CCF modeling framework. Here, the modeling framework is centered around the development of interconnected meshes of the node-link-basin using the Interconnected Channel and Pond Routing (ICPR) model. The modeling framework has been built for a complex drainage network, consisting of tidal creeks, tidal channels, underground sewer networks, and detention ponds in Charleston Peninsula, SC. The floodplain dynamics of the urbanized peninsula are modeled by a high-resolution LiDAR-derived Digital Elevation Model (DEM) and Digital Surface Model (DSM), and overland flow is simulated by energy balance, momentum balance, or diffusive wave methods. The performance of the CCF model is tested for the 2015 SC major flood and 2021 tidal flood events. The momentum balance-based CCF model shows 98.35% efficiency in capturing street-level flooding location and the CCF model depicts that using the DSM potentially improves the simulation accuracy of the flood by 15-33% compared to LiDAR DEM. Moreover, it is found the momentum balance between surge arrival from a tidally influenced river and rainfall runoff plays an important role in flood dynamics in urbanized catchments. This study contributes to the existing knowledge of fine-scale floodplain dynamics in urban areas by enhancing the fully-coupled numerical representation of CCF processes.