Although autonomous vehicle (AV) technology is expected to bring dramatic societal, environmental, and economic benefits, the high vehicle cost might slow the adoption of AVs. This paper explores an infrastructure-enabled autonomous driving system, which is a promising remedy to the high cost of AVs. Specifically, the system combines vehicles and infrastructure in the realization of autonomous driving. Equipped with roadside sensing, computing, and communicating devices, an ordinary road can be upgraded into an automated road enabling autonomous driving service for vehicles with the minimum required on-board devices. The vehicle costs can thus be significantly reduced. We envision that automated roads will be deployed in transportation networks to serve a new type of vehicle called infrastructure-enabled autonomous vehicles (IEAVs), which can be driven autonomously only on automated roads but manually on ordinary roads. Therefore, IEAV users may experience inconvenience costs due to transitions between autonomous driving and manual driving, and the frequent switch will inevitably yield high inconvenience costs. Therefore, to minimize their individual travel cost, they have to decide whether to switch to the autonomous driving mode when heading to an automated road. Considering such a unique feature of IEAVs, we proposed a group of driving-mode-choice equilibrium conditions to describe IEAV drivers driving mode choice behaviors, in which we considered drivers travel time costs, service charges of autonomous driving, and inconvenience costs due to driving mode change. Combining traditional route-choice equilibrium conditions with the proposed driving-mode-choice equilibrium conditions, we developed a new user equilibrium (UE) model to describe the equilibrium flow distributions in a road network with automated roads and mixed-autonomy traffic. The UE model is formulated as a novel non-linear complementarity problem, and its solution existence is discussed. To solve the UE model, a network expansion method is proposed to reformulate the UE model as a standard path-based UE model. A route-swapping-based solution algorithm is then used to solve the reformulated UE model. Numerical studies are presented to demonstrate the proposed models and algorithms.