Reliability is becoming an increasingly important attribute of road networks. An approach to assess the performance reliability of road networks under nonrecurrent congestion is suggested. Nonrecurrent congestion can arise anywhere along the roadway; when it does arise, it suddenly reduces the capacity of the roadway and makes the traffic condition unstable. Confronted with such uncertain traffic conditions, commuters are known to exhibit different behaviors, namely, risk aversion, risk neutrality, and risk seeking, which are formulated by the expected disutility approach. Commuters are assumed to choose the path with minimal expected disutility. Consequently, a disutility-related multiclass user equilibrium might be achieved when the expected travel disutility between each origin-destination pair can be determined separately and uniquely. Because this disutility implies dissatisfaction or disliking with levels of variations of travel times perceived by commuters, it offers a suitable measure of network reliability for network design. The disutility-related multiclass user equilibrium is formulated as a nonlinear complementarity problem, which is a nonadditive path cost problem and can be solved by recently proposed path-based algorithms, Numerical examples are provided to illustrate the application of the proposed approach.