To optimize mitigation, preparedness, response, and recovery procedures for infrastructure systems, it is essential to use accurate and efficient means to evaluate system reliability against probabilistic events. The predominant approach to quantify the impact of natural disasters on infrastructure systems is the Monte Carlo approach, which still suffers from high computational cost, especially when applied to large systems. This article presents a deep learning framework for accelerating seismic reliability analysis, on a transportation network case study. Two distinct deep neural network surrogates are constructed and studied: (1) a classifier surrogate that speeds up the connectivity determination of networks and (2) an end‐to‐end surrogate that replaces modules such as roadway status realization, connectivity determination, and connectivity averaging. Numerical results from k‐terminal connectivity analysis of a California transportation network subject to a probabilistic earthquake event demonstrate the effectiveness of the proposed surrogates in accelerating reliability analysis while achieving accuracies of at least 99%.