Infrastructure systems have become increasingly vulnerable to various risks due to their growing interdependencies. The vulnerability analysis of Interdependent Infrastructure Systems (IISs) is crucial for enhancing system resilience against threats. This paper proposes a global vulnerability assessment model by considering the interplay between the attack strength of different risks and the preparedness of infrastructure systems. Three load metrics, Degree-based load, Betweenness-based load, and Flow-based load are adopted to evaluate the vulnerability of IISs. The vulnerability assessment model incorporates both inner- and inter-networks cascading failures to examine the impact of tolerance parameters on global vulnerability. Moreover, critical components are identified by analyzing N-1 scenarios. The results indicate that the vulnerability of IISs assessed by the flow-based load metric can reflect the real-world performance of service-providing IISs. Adjusting the tolerance parameter proves to be effective in mitigating the spread of failures. The vulnerability distribution of IISs can assist stakeholders in identifying critical components to protect for safeguarding IISs against attacks.