This paper proposes a reliability-based optimal scheduling model of integrated microgrids. The proposed model is capable of delivering optimal scheduling of each individual microgrid and aggregated system. In addition, it is compatible with both grid-connected and islanded operation modes. The developed problem formulation of the proposed model takes into account the reliability indices SAIDI, SAIFI, and CAIDI to evaluate the reliability of the integrated system. Numerical simulations on a modified IEEE-33 bus test system, involving four integrated microgrids, were performed to investigate the advantages and the robustness of the developed model. Furthermore, the impact of merging Battery Energy Storage Systems (BESSs) on the optimization outcome is examined, which demonstrates its significant effectiveness in improving the power systems' reliability.