Resilient infrastructure systems are essential for continuous and reliable functioning of social and economic systems. Taking advantage of network theory, this paper models street network, water supply network, power grid and information infrastructure network as layers that are integrated into a multilayer network. The infrastructure interdependencies are described using five basic dependence patterns of fundamental network elements. Definitions of dynamic cascading failures and recovery mechanisms of infrastructure systems are also established. The main contribution of the paper is a new infrastructure network resilience measure capable of addressing complex infrastructure system, as well as network component (layer) interdependences. The new measure is based on infrastructure network performance, proactive absorptive capacity and reactive restorative capacity, with three resilience features of network—robustness, resourcefulness, and rapidity. The quantitative resilience measure using dynamic space-time simulation model is illustrated with a multilayer infrastructure network numerical test, including different response strategies to floods of different scale. The results demonstrate that the resilience measure provides an evaluation method of various protection and restoration strategies that will optimize the performance of interdependent infrastructure system. The sector-specific decisions could not always lead to optimal system solutions, and systems approach offers significant benefits for increasing infrastructure system resilience. This study can assist municipal decision makers in (i) better understanding the effects of different response strategies on the resilience of interdependent infrastructure system, and (ii) deciding which strategy should be adopted under different types of disasters.