Natural or human-inflicted disasters may cause large-scale disruptions in the services of infrastructure networks including power, water, and telecommunication. Restoring the services of these infrastructures is vital in the aftermath of the disaster, so that search-and-rescue activities, relief transportation, and restoration efforts can be efficiently facilitated. On the other hand, operations of these infrastructures may depend on receiving services from one another, resulting in an interdependent network structure. Consequently, addressing the decisions of network reinforcement before the disaster and the repairs in its aftermath needs to take into account this interdependent structure, as well as the uncertainties arising from the timing, location, and magnitude of the disaster. This paper introduces the Stochastic Interdependent Infrastructure Reinforcement and Repair Problem, which considers the pre-disaster reinforcement of interdependent network components and post-disaster repair scheduling in an integrated manner. In making these decisions, the uncertainty on which network components will be disrupted is incorporated into the problem definition. The problem is modeled using scenario-based two-stage stochastic programming. A heuristic based on a genetic algorithm and partial optimization is proposed to solve realistically-sized instances of the problem. Computational experiments not only show that the heuristic is able to find near-optimal solutions within reasonable times, but also illustrate the ability of the approach to help derive managerial insights.