The concept of a multiplex network can be used to characterize the dispersal paths and states of different species in a patch habitat system. The multiplex network is one of three types of multilayer networks. In this study, the effect of a multiplex network on the long-term stable coexistence of species is investigated using the concept of metapopulation. Based on the mean field approximation, the stability analysis of a two-species system shows that, compared to the single layer network, the multiplex network is more conducive to the stable coexistence of species when one species has a stronger colonization ability. That is, in such a patch habitat system, if the dispersal paths of the stronger species are different than those of the weaker species, then the larger the heterogeneity of the dispersal network of the stronger species is, the more likely the long-term stable coexistence of species. This result provides a different perspective for understanding the biodiversity in heterogeneous habitats.