Natural hazards, such as storms, increasingly threaten interconnected critical infrastructure systems (CISs), necessitating integrated resilience strategies that account for interdependencies, cascading failures, and dynamic recovery. To contextualize the research within existing developments, a bibliometric analysis is conducted, revealing key trends and gaps in hazard-resilient CIS modeling. This article proposes a comprehensive framework that models interdependent behavior across power, telecommunication, and transportation networks under evolving storm conditions. A dedicated hazard engine captures the spatiotemporal progression of storms and simulates their direct and cascading impacts across infrastructure layers. The framework incorporates a dynamic, safety-aware restoration strategy that deploys repair crews and mobile energy resources in alignment with real-time storm conditions. The proposed framework is demonstrated through a case study inspired by the realistic infrastructure of Cyprus. Results show the model's ability to capture cascading disruptions, illustrate the operational effectiveness of dynamic restoration, and provide insights from sensitivity and tradeoff analyses.