In this study, a framework for identifying the damping ratio of a bridge using an instrumented three-mass test vehicle is proposed on the basis of a vehicle-bridge interaction system, in which the dynamic responses provided by the two unsprung masses are adopted to enhance the accuracy. For the instrumented three-mass test vehicle, several sensors are installed on it; the corresponding virtual scanning points on the bridge are used to identify the bridge damping ratio. To derive the damping formula, the free-decay responses of any two scanning points for a simply supported bridge are utilized. As for the finite element analysis, the scanning-point responses need to be filtered out, unlike the single-mode closed-form solutions. Particularly, the support effect is systematically investigated by considering a simply supported bridge and a two-span continuous bridge. The parametric study has shown the liability of the proposed framework via various practical factors in concern.