Life in the modern world depends on multiple critical services provided by infrastructure systems which are interdependent at multiple levels. To effectively respond to infrastructure failures, this paper proposes a model for developing optimal joint restoration strategy for interdependent infrastructure systems following a disruptive event. First, models for (i) describing structure of interdependent infrastructure system and (ii) their interaction process, are presented. Both models are considering the failure types, infrastructure operating rules and interdependencies among systems. Second, an optimization model for determining an optimal joint restoration strategy at infrastructure component level by minimizing the economic loss from the infrastructure failures, is proposed. The utility of the model is illustrated using a case study of electric-water systems. Results show that a small number of failed infrastructure components can trigger high level failures in interdependent systems; the optimal joint restoration strategy varies with failure occurrence time. The proposed models can help decision makers to understand the mechanisms of infrastructure interactions and search for optimal joint restoration strategy, which can significantly enhance safety of infrastructure systems.