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It is well known that the natural frequencies of a coupled vehicle–bridge interaction system are time-varying. While this knowledge is useful for applications in bridge health monitoring, it does not provide an understanding of the relations between the excitation and coupled system responses, nor leads to developments of effective control strategies to mitigate vibration. In this paper, a novel theoretical framework for the time-varying displacement transmissibility is developed using a time-frozen technique. The time–frequency characteristics of the transmissibility functions are investigated to gain fundamental understanding and insights of the coupling dynamics in relation to the matching of bridge and vehicle natural frequencies. An important aspect of the transmissibility formulation is that it leads to the development of physics-based vibration control strategies in the frequency domain. By applying the principle of fixed points from vibration absorber designs to the transmissibility functions, an optimally tuned vehicle suspension to mitigate bridge vibration is obtained. The tuning strategy depends only on a priori known structural parameters. Thus, the tuning strategy provides useful guidelines in practice and is shown to be effective in reducing the vibrations of both the moving vehicle and the bridge. This work paves a foundation for further research in the design of bridge-friendly vehicles via parameter tuning. [ABSTRACT FROM AUTHOR]