Urban integrated energy systems (UIES) have emerged as a promising solution to address the challenges of urban energy supply and consumption. However, UIES are vulnerable to extreme disasters, such as earthquakes, hurricanes, or floods, which can disrupt the energy infrastructure and lead to power outages and energy shortages. This study introduces a novel approach aimed at enhancing the resilience and load recovery capabilities of UIES in the face of extreme events. The proposed approach encompasses several key innovations, including the comprehensive coordination of local energy sources, prioritized restoration of critical loads, and a node-based modeling approach for gas and heat networks. Firstly, by fully integrating electricity, gas, and heat sources, the overall resilience of UIES is significantly improved, ensuring higher levels of load recovery even in the event of energy supply shortages. Secondly, the critical load recovery is prioritized by load classification, and the weights set can fully consider the connection status and load level of nodes to ensure priority provisioning of important node loads. In addition, the node-based modeling approach allows for accurate consideration of the flow of gas and heat in the pipe during modeling of the pipe energy storage. Finally, the case study section conducts simulation experiments with the UIES E33-G20-H6 test system to verify the effectiveness of the proposed approach and to demonstrate its potential in enhancing the post-disaster load recovery capability of UIES.