To investigate the resilience of interconnected critical infrastructures (CIs), a framework combining dynamic modeling and resilience analysis is proposed. Resilience is defined in this work as the capacity of a system to absorb the impacts of perturbations and recover quickly from disruptive states. It is seen as a property of the system, which depends on a number of design, operation, and control parameters. Within this framework, we introduce the concept of resilience regions in the parameters space: as long as the parameters values remain inside these regions during operation, the system visits only recoverable states or, in other words, it maintains nominal operation or recovers quickly to it. Based on this concept, we perform a resilience analysis of two interconnected critical infrastructures, a gas network and an electric power system. The analysis is performed by numerical calculation of the resilience conditions in terms of design, operation, and control parameters values for given failure scenarios. To render computationally feasible analysis, we resort to an abstract representation of the system dynamics by a linear model of switching dynamics. Although the high-level modeling adopted may suffer from predictive accuracy, the proposed framework can still provide valuable insights in the analysis of system resilience and its dependence on the design, operation, and control parameters under different failure scenarios, which can be valuable to inform the decision making process of CIs operators and other stakeholders.