The objective of this paper is to present a methodology that integrates Mixed Integer Programming (MIP) optimization methods into the calculation of metrics related to the reliability and resilience of a system of interdependent infrastructure networks, improving over mitigation strategies and vulnerability assessment that do not consider interdependence relations within an optimization framework. This methodology aims to provide tools to simulate diverse failure scenarios, assess their impact on the system's performance and recoverability, and quantify its sensitivity to adverse events. For the system's performance and recoverability measurement, this methodology builds upon the Interdependent Network Design Problem (INDP), which focuses on finding optimal recovery strategies given a disaster scenario. A computational experiment is carried out on simplified versions of the water, power, and gas networks in Shelby County, TN, which are geographically and physically interdependent. Results show that the approach permits comprehensive analysis about the fragility and vulnerability of a system of multiple correlated networks; hence, providing useful information for decision-makers to determine efficient mitigation actions directed to resilience enhancement.