Critical interdependent infrastructure networks such as water distribution, natural gas pipeline, electricity power, communication and transportation systems provide the essential necessities for societies and their utilization is the backbone of everyday processes such as production, health, convenience and many more. Often cascading dysfunctionality or disruption in these critical infrastructure networks triggers chain reactions of blackouts or blockages through the system of highly interconnected infrastructure networks and the inevitable collapse of surrounding societies. For the planning of restoration processes and resilience of these, social aspects and demographics should also be considered to assign and mitigate the possible social risks associated with these disruptions. Additionally, it is crucial to identify the most critical components of these networks which are the components that have the largest impact on the performance of both their and other networks that are operationally dependent. These critical components have the largest impact on society in terms of serving its needs so that its recovery can be completed in a timely manner after a disruption. This research studies the restoration planning of critical interdependent infrastructure networks after a possible disruptive event by mainly emphasizing on the vulnerability indices of interacting society. The methodology integrates (i) a resilience-driven multi-objective mixed-integer programming formulation to schedule the restoration process of disrupted network components in each network, and (ii) a component importance measure that quantifies the impact of equitable restoration activities on components with (iii) an index of social vulnerability that is geographically distributed. An illustrative example of the proposed integrated model that focuses on studying the community resilience in Shelby County, TN, United States is also represented.