Cooperative driving of connected and automated vehicles (CAVs) has attracted extensive attention and researchers have proposed various approaches. However, existing approaches are limited to small-scale isolated scenarios and gaps remain in network-wide cooperative driving, especially in routing. In this article, we decompose the network-level cooperative driving problem into two dominant sub-problems and accordingly propose a bi-level network-wide cooperative driving approach. The dynamic routing problem is considered in the upper level and we propose a multi-agent deep reinforcement learning (DRL) based routing model. The model can promote the equilibrium of network-wide traffic through distributed self-organized routing collaboration among vehicles, thereby improving efficiency for both individual vehicles and global traffic systems. In the lower level, we focus on the right-of-way assignment problem at signal-free intersections and propose an adaptive cooperative driving algorithm. The algorithm can adaptively evaluate priorities of different lanes, and then uses the lane priorities to guide the Monte Carlo tree search (MCTS) for better right-of-way assignments. Essentially, the upper level determines which conflict areas the vehicles will pass through, and the lower level addresses how the vehicles use the limited road resources more efficiently in each conflict area. The experimental results show that the upper and lower levels complement each other and work together to significantly improve the network-wide traffic efficiency and reduce the travel time of individual vehicles. Moreover, the results demonstrate that microscopic and mesoscopic cooperative driving behaviors of vehicles can significantly benefit the macroscopic traffic system.