The communication, computer and transportation systems can all be modelled as a network composed of vertices and links. To economically and efficiently improve network reliability, the interactions of these coupled two links regarding network failure must be analyzed. Therefore, under the condition that link failures appear according to a saturated nonhomogeneous Poisson process, we propose a novel method to calculate the joint failure importance (JFI) for the two links given , which can characterize how the links interact in contributing to network failure. Specifically, based on the knowledge of combinatorial counting, the probabilities that arbitrary two links are in four different states are derived. Then, combining the joint D-spectrum for the two links, a formula to calculate the JFI is established. Theoretical analysis shows that when time t approaches zeros or infinity, the interaction effects between the two links are more and more weak. Since the exact computing for JFI is NP-hard problem, we provide a Monte-Carlo algorithm to evaluate JFI. Finally, we perform a numerical example of a road network to demonstrate the method for computing JFI. The numerical results show that proposed method for computing JFI can efficiently account for the interaction of links on network failure.