Communication networks as smart infrastructure systems play an important role in smart girds to monitor, control, and manage the operation of electrical networks. However, due to the interdependencies between communication networks and electrical networks, once communication networks fail (or are attacked), the faults can be easily propagated to electrical networks which even lead to cascading blackout; therefore it is crucial to investigate the impacts of failures of communication networks on the operation of electrical networks. This paper focuses on cascading failures in interdependent systems from the perspective of cyber-physical security. In the interdependent fault propagation model, the complex network-based virus propagation model is used to describe virus infection in the scale-free and small-world topologically structured communication networks. Meanwhile, in the electrical network, dynamic power flow is employed to reproduce the behaviors of the electrical networks after a fault. In addition, two time windows, i.e., the virus infection cycle and the tripping time of overloaded branches, are considered to analyze the fault characteristics of both electrical branches and communication nodes along time under virus propagation. The proposed model is applied to the IEEE 118-bus system and the French grid coupled with different communication network structures. The results show that the scale-free communication network is more vulnerable to virus propagation in smart cyber-physical grids.