This paper proposes a novel adaptive robust optimization (ARO)-based mathematical framework for resilience enhancement of interdependent critical infrastructure (CI) systems against natural hazards (NHs). In this framework, the potential impacts of a specific NH on an infrastructure are firstly evaluated, in terms of failure and recovery probabilities of system components; these are, then, fed into a two-stage ARO model to determine the optimal planning of resilience strategies under limited investment budget, anticipating the most-likely worst realization of the uncertainty of component failures under the NH. For its exact solution, a decomposition method based on simultaneous column-and-constraint generation is adopted. The approach is applied to a case study concerning the resilience of interdependent power and gas networks subject to (simulated) wind storms. The numerical results demonstrate the effectiveness of the proposed framework for the optimization of the resilience of interdependent CIs under hazardous events; this provides a valuable tool for making informed pre-hazard preparation decisions. The value of a coordinated pre-hazard planning that takes into account CI interdependencies is also highlighted.