In automotive engineering, designing for optimal vehicle dynamics is challenging due to the complexities involved in analysing the behaviour of a multibody system. Typically, a simplified set of dynamics equations for only the key bodies of the vehicle such as the chassis and wheels are formulated while reducing their degrees of freedom. In contrast, one could employ high-fidelity multibody dynamics simulation and include more intricate details such as the individual suspension components while considering full degrees of freedom for all bodies; however, this is more computationally demanding. Also, for gradient-based design optimization, computing adjoints for different objective functions can be more challenging for the latter approach, and often not feasible if an existing multibody dynamics solver is used. We propose a mixed-fidelity multidisciplinary approach, in which a simplified set of dynamics equations are used to model the whole vehicle while incorporating a high-fidelity multibody suspension module as an additional coupled discipline. We then employ MAUD (modular analysis and unified derivatives) to combine analytical derivatives based on the dynamics equations and finite differences obtained using an existing multibody solver. Also, we use a collocation method for time integration, which solves for both the system trajectory and optimal design variables simultaneously. The benefits of our approach are shown in an experiment conducted to find optimal vehicle parameters that optimize ride comfort and driving performance considering vertical vehicle dynamics.