Background: The identification of cancer driver genes and key molecular pathways has been the focus of large-scale cancer genome studies. Network-based methods detect significantly perturbed subnetworks as putative cancer pathways by incorporating genomics data with the topological information of PPI networks. However, commonly used PPI networks have distinct topological structures, making the results of the same method vary widely when applied to different networks. Furthermore, emerging context-specific PPI networks often have incomplete topological structures, which pose serious challenges for existing subnetwork detection algorithms. Methods: In this paper, we propose a novel method, referred to as MultiFDRnet, to address the above issues. The basic idea is to model a set of PPI networks as a multiplex network to preserve the topological structure of individual networks, while introducing dependencies among them, and, then, to detect significantly perturbed subnetworks on the modeled multiplex network using all the structural information simultaneously. Results: To illustrate the effectiveness of the proposed approach, an extensive benchmark analysis was conducted on both simulated and real cancer data. The experimental results showed that the proposed method is able to detect significantly perturbed subnetworks jointly supported by multiple PPI networks and to identify novel modular structures in context-specific PPI networks.