A wide range of complex systems can be modeled as networks with corresponding constraints on the edges and nodes, which have been extensively studied in recent years. Nowadays, with the progress of information technology, systems that contain the information collected from multiple perspectives have been generated. The conventional models designed for single perspective networks fail to depict the diverse topological properties of such systems, so multilayer network models aiming at describing the structure of these networks emerge. As a major concern in network science, decomposing the networks into communities, which usually refers to closely interconnected node groups, extracts valuable information about the structure and interactions of the network. Unlike the contention of dozens of models and methods in conventional single-layer networks, methods aiming at discovering the communities in the multilayer networks are still limited. In order to help explore the community structure in multilayer networks, we propose the multilayer edge mixture model, which explores a relatively general form of a community structure evaluator from an edge combination view. As an example, we demonstrate that the multilayer modularity and stochastic blockmodels can be derived from the proposed model. We also explore the decomposition of community structure evaluators with specific forms to the multilayer edge mixture model representation, which turns out to reveal some new interpretation of the evaluators. The flexibility and performance on different networks of the proposed model are illustrated with applications on a series of benchmark networks.