With the development of autonomous driving technology, Connected Autonomous Vehicles (CAVs) will experience a long-term mixed driving phase with traditional Human-piloted Vehicles (HVs). How to effectively coordinate the driving behaviors of these two types of vehicles to improve the operational efficiency of the mixed traffic system is a significant challenge facing intelligent transportation systems today. To address this issue, this study proposes a cooperative control strategy for mixed traffic flow. This strategy, based on the different route choice characteristics of the vehicles and considering the impact of CAVs on road capacity, constructs a UE-SO hybrid traffic equilibrium model, which is formulated and solved as a variational inequality problem. Subsequently, an iterative weighting algorithm (Method of Successive Averages, MSA) was used to solve the model. Numerical experiments on the SiouxFalls network demonstrate the effectiveness of the algorithm. The results show that as the market penetration rate of CAVs increases, the total system travel time significantly decreases; a reasonable CAV penetration rate and cooperative control strategy can significantly improve the road network capacity.