Many areas of the world are prone to multiple hazards that can be concurrent/non-concurrent and dependent/independent. Infrastructure systems located in such areas will likely be subjected to more than one hazard in their lifetime. The damage due to such hazards on electric power systems is well documented. Over the years, strategies to mitigate single hazards have been proposed for electric power systems. However, accurate long-term decisions on investment in risk mitigation strategies require the consideration of multiple hazards that can impact a system over its lifespan. Therefore, there is a need to investigate the cost-effectiveness of mitigation strategies in reducing risks to infrastructure systems that are vulnerable to multiple hazards given the constraints on resources. This requires a comprehensive multi-hazard risk assessment approach. This paper presents a framework for investigating the effectiveness of multi-hazard risk mitigation strategies for electric power systems subjected to seismic and hurricane wind hazards. The framework includes probabilistically weighted deterministic hazard analysis model, component vulnerability models, topologically based system performance model, component importance measure appropriate for networked systems, and life cycle cost analysis. A notional electric power network assumed to be located in Charleston, SC, and New York, NY, is used to demonstrate the proposed framework.