Coupling cyber and physical systems gives rise to numerous engineering challenges and opportunities. An important challenge is the contagion of failure from one system to another, that can lead to large scale cascading failures. On the other hand, self-healing ability emerges as a valuable opportunity where the overlay cyber network can cure failures in the underlying physical network. To capture both self-healing and contagion, we introduce a factor graph representation of inter-dependent cyber-physical systems in which factor nodes represent various node functionalities and the edges capture the interactions between the nodes. We develop a message passing algorithm to study the dynamics of failure propagation and healing in this representation. Through applying a fixed-point analysis to this algorithm, we investigate the network reaction to initial disruptions. Our analysis provides simple yet critical guidelines for choosing network parameters to achieve resiliency against cascading failures.