In this paper, we evaluate the robustness and recovery of connected critical infrastructures (CIs) under a system-of-systems (SoS) framework taking into account: (1) the dependencies among the components of an individual CI and the interdependencies among different CIs; (2) the variability in component performance, by a multistate model; and (3) the epistemic uncertainty in the probabilities of transitions between different components states and in the mean values of the holding-times distributions, by means of intervals. We adopt the goal tree success tree–dynamic master logic diagram (GTST–DMLD) for system modeling and perform the quantitative assessment by Monte Carlo simulation. We illustrate the approach by way of a simplified case study consisting of two interdependent infrastructures (electric power system and gas network) and a supervisory control and data acquisition (SCADA) system connected to the gas network.