Multiplex networks have emerged as a promising approach for modeling complex systems, where each layer represents a different mode of interaction among entities of the same type. A core task in analyzing these networks is to identify the community structure for a better understanding of the overall functioning of the network. While different methods have been proposed to detect the community structure of multiplex networks, the majority deal with extracting the consensus community structure across layers. In this paper, we address the community detection problem across two closely related multiplex networks. For example in neuroimaging studies, it is common to have multiple multiplex brain networks where each layer corresponds to an individual and each group to different experimental conditions. In this setting, one may be interested in both learning the community structure representing each experimental condition and the discriminative community structure between two groups. In this paper, we introduce two discriminative community detection algorithms based on spectral clustering. The first approach aims to identify the discriminative subgraph structure between the groups, while the second one learns the discriminative and the consensus community structures, simultaneously. The proposed approaches are evaluated on both simulated and real world multiplex networks.