Integral Control strategy for vehicle chassis systems had been of great interest for vehicle designers in the last decade. This paper represents the interaction of longitudinal control and lateral control. In other words the traction control system and handling control system. Definitely, tire properties are playing a vital role in such interaction as it is responsible for the generated forces in both directions.A seven degrees of freedom half vehicle model is derived and used to investigate this interaction. The vehicle body is represented as a rigid body with three degrees of freedom, lateral and longitudinal, and yaw motions. The other four degrees are the two rotation motion of the front wheel and the rear wheel. This two motions for each wheel are spin motion and the steering motion. The traction controller is designed to modulate engine torque through adjusting the throttle angle of the engine upon utilized adhesion condition at the driving road wheels. The active four steering (4WS) control system is designed to enhance vehicle lateral dynamics through controlling rear steer angle. The optimal and fuzzy logic control theories are used to design the system controllers. The integrated model connects the two systems via the Magic Formula Tire Model to represent the tire non-linearity during augmented longitudinal and lateral dynamic attitudes.The simulation results helped to understand the effects of each chassis system on the other system. Moreover, this simulation highlights the importance of taking these effects into account when designing the integrated controller for improved vehicle overall performance.