As critical components of urban infrastructure, water and power supply networks play important roles by supplying water and power for living and production to maintain daily operation in urban areas. In previous earthquakes, seismic damage to these facilities has severe impact on urban emergency rescue, firefighting, and health care. Therefore, it is of great significance to ensure the seismic resilience of water and power supply networks. A new methodology based on network flow theory was proposed for the seismic resilience analysis of water and power supply networks with highly functional interdependent characteristics. First, the optimal objective function of the collaborative recovery of water and power supply networks was established, and the constraint conditions of the post-earthquake functional recovery of water and power supply networks were presented according to the network flow method. On the basis of the Gurobi solver, the coupled model was solved by the mixed integer programming method. The proposed method could effectively evaluate the seismic performance of different parts of each network. Moreover, the repair tasks could be reasonably distributed according to the existing repair resources to realize the optimal recovery of the interdependent networks. Results show that due to the uncertainties of physical damage of the components of water and power supply networks, the recovery process of water and power supply networks exhibited significant discreteness, and the discreteness changed over time. On average, the recovery speed of power grids was faster than that of water supply networks.