Simulation testing is critical for the development and optimization of connected and autonomous vehicle (CAV) driving systems. Existing simulation tools for autonomous driving testing generally focus on single-vehicle-based perception, decision, and control. Nevertheless, cooperative maneuvering among CAV and human-driven vehicles is of utmost importance in many high-value scenarios, e.g., intersections, platooning, and bottlenecks. To this end, this article aims to establish a comprehensive and realistic co-simulation framework that combines both vehicle and traffic simulation. For the sake of presentation and without loss of generality, CARLA is employed for vehicle simulation as it features high-fidelity vehicle dynamics models, while Simulation of Urban Mobility is employed for traffic simulation as it provides advanced traffic models. Further, vehicle trajectory extraction technology is applied to extract vehicle trajectories from videos and use them as an input of the co-simulation framework. Moreover, three different scenarios comprising the presence of obstacles on the highway, congested city intersections, and complete CAV testing are described to verify the rationality of the framework. The real data-driven, full-chain co-simulation testing method proposed in this article can provide a realistic virtual environment for testing decision- and motion-planning level vehicular functions of CAVs.