Infrastructure systems are essential to the functioning of contemporary societies and economies. A major disruption to the built environment can lead to severe public safety issues and economic losses. Within the past few decades, modern control and information technologies have been rapidly developed in an attempt to improve the reliability of individual utility systems by exchanging technologies across them. One of the major ramifications is the emergence of interdependencies among these critical infrastructure systems, especially when facing major disruptions. Failure of an individual system becomes more likely to affect the functionality of other interconnected infrastructure systems. In order to mitigate such consequences, the mechanics of interdependencies and failure propagation among the systems must be understood. This research focuses on the development of a framework for probabilistically quantifying interdependent responses of two essential infrastructure systems - telecommunication and electric power systems - subjected to seismic hazards, which are one of the most powerful and geographically extensive threats. The study explores the effects of seismic hazards beyond the obvious seismic-induced physical damage to utility system facilities. In particular, the seismic evaluation of telecommunication systems considers the degradation of system performance due to physical damage and the abnormally high usage demands in telecommunication systems expected after catastrophic earthquakes. Specifically, a newly developed seismic-induced congestion model is proposed, and the probabilistic formulations of the critical interdependencies across telecommunication and power systems are presented in a probabilistic framework. The study illustrates the procedure for fragility analysis of interdependent systems and presents a practical application through a test bed implementation in Shelby County, TN. From this study, telecommunication systems are found to be very vulnerable to seismic-induced congestion. The electric power interdependencies amplify the degradation in telecommunication systems up to 50% in their vulnerability while electric power operations are heavily dependent upon telecommunication infrastructures and the fragility median of electric power system observability can decrease by 30%. The study also indicates up to 100% overestimation of the independent fragility analysis and the results reveal the relationship between system topology and the sensitivity of system performance to the intensity of interdependencies. The proposed methodology is expected to be a valuable tool for decision making in evaluating seismic mitigation strategies and also to provide the foundation for future studies on interdependent responses of other critical infrastructures.