We study the dynamics of an air bubble bouncing at a liquid/liquid/gas interface, which we refer to as a compound interface. When a bubble interacts with a thin layer of oil on top of bulk water, the oil layer modifies the interfacial properties and thus the entire process of bouncing and bubble bursting. The influence on the bubble motion is experimentally and numerically investigated. Based on the coefficient of restitution and the damping rate of the bubble velocity profile, the damping increases with the oil layer thickness and viscosity. In addition, the effect of the oil layer thickness is more prominent for high-viscosity oil. Furthermore, a reduced-order mass–spring–damper model is proposed to describe the bubble bouncing at the compound interface, which predicts the time of the first contact of the bubble with the interface and agrees well with the experimental results. Such a model also captures the general experimental trends of the coefficient of restitution for the multiphase system. Our work contributes to a further understanding of the collision and coalescence of bubbles with a compound interface.