Community structures exist in many infrastructure networks (e.g., electric power, water distribution, natural gas) where each network is partitioned into sets of densely connected components with sparse connections between them. Such community structures are formed in infrastructure networks based on physical connections within each network or their spatial characteristics, among others. However, infrastructure networks depend on one another for proper functionality. Though the interdependencies across infrastructure networks can improve their efficiency, they make them highly vulnerable to any disruption. This work studies the restoration problem of community structures in a system of interdependent infrastructure networks following a disruptive event from the perspective of their resilience. A restoration model is proposed using mixed-integer programming to restore community structures in each infrastructure networks such that the resilience of the system of interdependent infrastructure networks is enhanced considering their interdependencies. Furthermore, we propose and discuss multiple community structures importance measures to prioritize their restoration process. Such measures could be used in solving the restoration model of community structures. The proposed restoration model and importance measures are illustrated through a generated system of interdependent infrastructure networks.