Multimodal arterial signal coordination for buses and passenger vehicles can improve arterial travel smoothness and efficiency. However, uncertainty in bus operations requires signal priority at intersections, which impacts coordination and increases stop times for other traffic types. Therefore, this study proposes a stochastic priority-integrated signal coordination (SPIC) method. It includes an offline stochastic programme to determine the arterial signal coordination, i.e. cycle length and offsets, considering the stochastic signal priority, and an online mixed-integer nonlinear programme to determine the signal priority together with the bus arrival and departure times at and from stops and intersections in a connected vehicle environment. A scenario-based heuristic algorithm is proposed to solve the SPIC efficiently. Numerical studies have validated that SPIC can improve the efficiency of buses and passenger vehicles. Sensitivity analyses show that the SPIC effectively reduces delays with fluctuations in the bus travel time, dwell time, and passenger vehicle demands.