Extreme natural hazards such as floods, hurricanes and earthquakes can cause catastrophic failures of infrastructure assets and networks. Understanding the risks due to natural hazards on large-scale infrastructures presents several challenges due to ubiquitous uncertainties and inherent system complexities. This study proposes a comprehensive system-of-systems approach for building different components of the risk problem and combining them into a cohesive framework. We build and apply analytical concepts, theoretical and simulation models and data tools to develop the integrated risk analysis framework. The system-of-systems approach adopted here produces: (i) a mathematical formalisation of the risk analysis framework that deals with quantifying probabilistic hazards, interdependent infrastructure failure probabilities, disruption evaluation, and economic loss estimation, and (ii) a demonstrable framework that establishes a unified implementation for reliability analysis, vulnerability assessment, and risk analysis. A case study with interdependent national electricity and railway networks and spatial hazard events shows the results of the risk calculations and provide valuable insights into understanding and interpreting national-scale infrastructure risk.