<p>Previous studies on the collaborative control of signals and vehicles—including both connected autonomous vehicles and connected autonomous buses (CABs)—in networked intersections predominantly emphasized enhancing the stability of heterogeneous flows to augment intersection efficiency. However, these studies often overlooked the crucial criterion of CAB punctuality. Addressing this significant gap, the present paper introduces a CAB travel time estimation model and a punctuality evaluation index into optimization problems to ensure the adherence to bus schedules. A mixed integer linear programming model, incorporating binary signal state variables, is established with the goals of heterogeneous platoon operation stability, bus arrival punctuality, and intersection efficiency. To ensure efficient model resolution, binary auxiliary logic variables are employed to linearize the relationship between signal transitions and the operational state of the heterogeneous flow. An evaluation is conducted using a standard four-arm intersection, wherein parameters like CAB proportions and overall traffic volume are varied for comprehensive testing. Simulation outcomes compellingly show that the proposed approach markedly improves CAB punctuality and diminishes energy consumption by enhancing heterogeneous flow stability. Specifically, there is an average increase of 22.3% in punctuality and a reduction of at least 15.1% in energy consumption.</p>