The number of EVs and charging facilities is expected to increase significantly in the near future, further coupling the existing transportation system with the power system. This may bring new stresses and risks to such system of systems. This paper presents a mathematical framework to analyze the resilience of an electrified road network (ERN) subject to potential failures of its supporting fast-charging stations (FCSs). Within this framework, a novel linear optimization model is proposed for the first time to solve the system optimal dynamic traffic assignment problem of ERN. The characteristics considered in the modeling framework include the location, capacity, and charging speed of FCSs, as well as the driving range, charging time and state of charge (SoC) of EVs. The linear model is proposed based on the cell transmission model. It is used as the first stage model to assign the traffic under normal FCS operations. A second stage model is, then, extended to minimize the total travel time after the stochastic occurrence of FCS failures, i.e., in the failure and recovery phases. Two metrics are considered to quantify the ERN performance and the impacts of FCS failures. A numerical example is studied to illustrate the usefulness of the proposed framework for analyzing ERN resilience. The results show that deploying FCSs near the highway entrances and maintaining their operation are relevant factors to enhance the system's resilience. The analysis can provide guidelines to the system operators for effective management of the ERN operation and identify resilience-critical FCSs for system resilience improvement.