Critical infrastructure networks are geographically distributed systems spanning multiple scales. These networks are increasingly interdependent for normal operations, which causes localized asset failures from natural hazards or man-made interference to propagate across multiple networks, affecting those far removed from an initiating failure event. This paper provides methodology to identify such failure propagation effects by quantifying the spatial variability in magnitude, frequency, and disruptive reach of failures across national infrastructure networks. To achieve this, we present methodology to combine functionally interdependent infrastructure networks with geographic interdependencies by simulating complete asset failures across a national scale grid of spatially localized hazards. A range of metrics are introduced to compare the systemic vulnerabilities of infrastructure systems and the resulting spatial variability in both the potential for initiating widespread failures and the risk of being impacted by distant hazards. We demonstrate the approach through an application in New Zealand of infrastructures across the energy (electricity, petroleum supply), water and waste (water supply, wastewater, solid waste), telecommunications (mobile networks), and transportation sectors (passenger rail, ferry, air, and state highways). In addition to identifying nationally significant systemic vulnerabilities, we observe that nearly half (46%) of the total disruptions across the simulation set can be attributed to network propagation initiated asset failures. This highlights the importance in considering interdependencies when assessing infrastructure risks and prioritizing investment decisions for enhancing resilience of national networks.