Managing mixed traffic comprising human-driven and robot vehicles (RVs) across large-scale networks presents unique challenges beyond single-intersection control. This paper proposes a reinforcement learning framework for coordinating mixed traffic across multiple interconnected intersections. Our key contribution is a neighbor-aware reward mechanism that enables RVs to maintain balanced distribution across the network while optimizing local intersection efficiency. We evaluate our approach using a real-world network, demonstrating its effectiveness in managing realistic traffic patterns. Results show that our method reduces average waiting times by 39.2% compared to the state-of-the-art single-intersection control policy and 79.8% compared to traditional traffic signals. The framework's ability to coordinate traffic across multiple intersections while maintaining balanced RV distribution provides a foundation for deploying learning-based solutions in urban traffic systems.