The longitudinal motion control of automotive vehicles is heavily reliant on information about the time-varying tire road friction coefficient. In the presence of varying road roughness profiles, the effective vertical load on each wheel varies dynamically, influencing the tire friction. In this paper, we integrated the vertical and longitudinal dynamics of a quarter wheel to form an integrated nonlinear model. In the modeled dynamics, the time-varying random road profile and the tire friction are treated as unknown inputs. To estimate these unknown inputs and states simultaneously, a combination of nonlinear Lipschitz observer and modified super-twisting algorithm (STA) observer is developed. Under Lipschitz conditions for the nonlinear functions, the convergence of the estimation error is established. Simulation results performed with the high-fidelity vehicle simulation software CarSim demonstrate the effectiveness of the proposed scheme in the estimation of states and unknown inputs.