Road and power systems are the backbone of a city. With rapid urbanization, the two facilities are highly interconnected. The vulnerability of the Interdependent Road-Power Systems (IRPS) can cause large-scale failures and even catastrophic disasters with severe social and economic consequences. In this paper, the IRPS is composed of nodes, edges, and links between layers. Distance between junction nodes with traffic lights in the Road Network (RN) and power stations in the Power Network (PN) is used to construct the functional interdependence. A non-linear load-capacity model is proposed to describe the capacity and ability of IRPS to handle allocated loads. Considering the current ability of neighbor nodes, we propose an intelligent node loads redistribution rule. The vulnerability level of RN, PN, and IRPS are measured, respectively. A case study based on real road data in Xi'an, China is conducted to validate the model. Results show that: (1) The redistribution rule is an important tool to decrease the vulnerability of the RN, while the capacity tolerance degree is more influential for the PN. (2) Parameters for the global vulnerability, there is a cross-impact between the capacity tolerance parameters.