Under adverse weather conditions, visibility and the available pavement friction are reduced. The improper selection of speed on curved road sections leads to an unreasonable distribution of longitudinal and lateral friction, which is likely to cause rear-end collisions and lateral instability accidents. This study considers the combined braking and turning maneuvers to obtain the permitted vehicle speed under rainy conditions. First, a braking distance computation model was established by simplifying the relationship curve between brake pedal force, vehicle braking deceleration, and braking time. Different from the visibility commonly used in the meteorological field, this paper defines "driver's sight distance based on real road scenarios" as a threshold to measure the longitudinal safety of the vehicle. Furthermore, the lateral friction and rollover margin is defined to characterize the vehicle's lateral stability. The corresponding relationship between rainfall intensity-water film thickness-road friction is established to better predict the safe speed based on the information issued by the weather station. It should be noted that since the road friction factor of the wet pavement not only determined the safe vehicle speed but also be determined by the vehicle speed, so we adopt Ferrari's method to solve the quartic equation about permitted vehicle speed. Finally, the braking and turning maneuvers are considered comprehensively based on the principle of friction ellipse. The results of the TruckSim simulation show that for a single-unit truck, running at the computed permitted speed, both lateral and longitudinal stability meet the requirements. The proposed permitted vehicle speed model on horizontal curves can provide driving guidance for drivers on curves under rainy weather or as a decision-making basis for road managers.