Understanding and characterizing the vulnerability of urban infrastructures, which refers to the engineering facilities essential for the regular running of cities and that exist naturally in the form of networks, is of great value to us. Potential applications include protecting fragile facilities and designing robust topologies, etc. Due to the strong correlation between different topological characteristics and infrastructure vulnerability and their complicated evolution mechanisms, some heuristic and machine-assisted analysis fall short in addressing such a scenario. In this paper, we model the interdependent network as a heterogeneous graph and propose a system based on graph neural network with reinforcement learning, which can be trained on real-world data, to characterize the vulnerability of the city system accurately. The presented system leverages deep learning techniques to understand and analyze the heterogeneous graph, which enables us to capture the risk of cascade failure and discover vulnerable infrastructures of cities. Extensive experiments with various requests demonstrate not only the expressive power of our system but also transferring ability and necessity of the specific components.