This study presents a generalized model of mixed elastohydrodynamic lubrication, in which the dimensional Reynolds equation is discretized according to a modified differential scheme based on the full analysis of the pressure balance within the lubrication region. The model is capable of a wide range of lubrication regimes from fully hydrodynamic down to boundary lubrication, and both the steady-state and the time-dependent conditions can be considered. A simplified computational procedure is proposed for elliptical contacts without the ellipticity parameters specified. The evolution of lubrication behavior at startup and shutdown conditions is investigated and the transient effect of surface waviness is discussed. The model application is then extended to contacts of multilayered materials, and the effects of the layer stiffness and the fabrication methods on the stress fields and lubrication performance are analyzed. The conclusions may potentially provide some insightful information for the design and analysis of functional materials and their engineering structures.