The introduction of connected autonomous vehicles may bring opportunities and challenges to traditional traffic control instruments, like ramp metering. This paper starts by constructing the fundamental diagram for mixed-autonomy traffic based on the car-following behaviors of both connected autonomous vehicles and human-driven vehicles. Then, analyses are performed on the main factors that influence the critical velocity, critical density, and road capacity under mixed-autonomy traffic. Two methods named COE-HERO and TRLCRM are developed to support the implementations of coordinated ramp metering for freeways with mixed-autonomy traffic. The COE-HERO method enhances the HERO method by incorporating a critical occupancy estimation module. Both COE-HERO and TRLCRM consider dynamic traffic flow parameters of mixed-autonomy traffic. The TRLCRM method is a reinforcement learning-based approach with a two-stage training framework, enabling it to adapt to varying mixed-autonomy demand scenarios. Extensive microscopic simulations show that the learning-based TRLCRM method can effectively alleviate bottleneck congestion and is robust to deal with various traffic scenarios. The COE-HERO method performs better than the HERO method, indicating the necessity of critical occupancy estimation in the implementations of coordinated ramp metering.