This article proposes an approach based on the stochastic process and approximate dynamic behavior for modeling cascading failures of the cyberphysical power system (CPPS) considering component multistate failures. Our approach focuses on modeling the coupling effects of interdependencies of the integrated power and communication networks, including control and power supply dependencies as well as the effects of the degradation of one network performance on the other. Nine failure states of each component and the performance/capacity degradation in different failure states are incorporated into the modeling approach. The state transitions between nine failure states are modeled as a discrete time Markov process whose transition probabilities are time-varying. In addition, the article proposes a new robustness measure for multistate CPPS, which integrates the information of the local and global topology, the damage state of components, as well as the performance degradation of the CPPS. The system that couples the IEEE 118-bus model with a small-world communication network is used as a testbed to demonstrate the feasibility and effectiveness of the proposed modeling approach, and the comparison with existing robustness measures shows the superiority of the proposed measure.