The transportation sector contributes up to 27% of the total greenhouse gas (GHG) emissions in the United States; on-road transportation is responsible for 84% of the entire sector, implying that vehicles are a major cause of global warming. To understand the fuel energy dissipated through a vehicle’s suspension and tires, researchers have recently examined stochastic pavement models combined with mechanics-based vehicle models. These approaches assume the pavement is nondeformable with a certain random roughness level. In this paper, a pavement–vehicle interaction model is developed that can accommodate both road roughness and the deflection of rigid pavement. A quarter-car model is considered to represent the vehicle, a filtered white noise model is used to characterize the road roughness, and a two-elastic layered foundation (Euler–Bernoulli beam for the top pavement and Winkler foundation for the subgrade) is employed to simulate the rigid pavement. Subsequently, an augmented state-space representation is formulated for the entire pavement–vehicle system. The Lyapunov equation governing the covariance of the response is solved to obtain the energy dissipation of the vehicle’s suspension and tires. Finally, examples are presented and compared with the nondeformable pavement model to understand the impact of rigid pavement deformation on vehicle fuel energy dissipation.