How are ecological systems assembled? Identifying common structural patterns within complex networks of interacting species has been a major challenge in ecology, but researchers have focused primarily on single interaction types aggregating in space or time. Here, we shed light on the assembly rules of a multilayer network formed by frugivory and nectarivory interactions between bats and plants in the Neotropics. By harnessing a conceptual framework known as the integrative hypothesis of specialization, our results suggest that phylogenetic constraints separate species into different layers and shape the network's modules. Then, the network shifts to a nested structure within its modules where interactions are mainly structured by geographic co-occurrence. Finally, organismal traits related to consuming fruits or nectar determine which bat species are central or peripheral to the network. Our results provide insights into how different processes contribute to the assemblage of ecological systems at different levels of organization, resulting in a compound network topology.