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Critical infrastructure networks are becoming increasingly interdependent which adversely impacts their performance through the cascading effect of initial failures. Failing to account for these complex interactions could lead to an underestimation of the vulnerability of interdependent critical infrastructure (ICI). The goal of this research is to assess how important interdependent links are by evaluating the interdependency strength using a dynamic network flow redistribution model which accounts for the dynamic and uncertain aspects of interdependencies. Specifically, a vulnerability analysis is performed considering two scenarios, one with interdependent links and the other without interdependent links. The initial failure is set to be the same under both scenarios. Cascading failure is modeled through a flow redistribution until the entire system reaches a stable state in which cascading failure no longer occurs. The unmet demand of the networks at the stable state over the initial demand is defined as the vulnerability. The difference between the vulnerability of each network under these two scenarios is used as the metric to quantify interdependency strength. A case study of a real power-water-gas system subject to earthquake risk is conducted to illustrate the proposed method. Uncertainty is incorporated by considering failure probability using Monte Carlo simulation. By varying the location and magnitude of earthquake disruptions, we show that interdependency strength is determined not only by the topology and flow of ICIs but also the characteristics of the disruptions. This compound system-disruption effect on interdependency strength can inform the design, assessment, and restoration of ICIs.