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Astrocytes critically shape whole-brain structure and function by forming extensive gap junctional networks that intimately and actively interact with neurons. Despite their importance, existing computational models of whole-brain activity ignore the roles of astrocytes while primarily focusing on neurons. Addressing this oversight, we introduce a biophysical neural mass network model, designed to capture the dynamic interplay between astrocytes and neurons via glutamatergic and GABAergic transmission pathways. This network model proposes that neural dynamics are constrained by a two-layered structural network interconnecting both astrocytic and neuronal populations, allowing us to investigate astrocytes' modulatory influences on whole-brain activity and emerging functional connectivity patterns. By developing a simulation methodology, informed by bifurcation and multilayer network theories, we demonstrate that the dialogue between astrocytic and neuronal networks manifests over fast-slow fluctuation mechanisms as well as through phase-amplitude connectivity processes. The findings from our research represent a significant leap forward in the modeling of glial-neuronal collaboration, promising deeper insights into their collaborative roles across health and disease states.