The impact of liquid droplets on nonwetting solid surfaces and their subsequent rebounds have been extensively studied in recent decades, largely because of their robustness in practical scenarios. However, most works were focused on impinging single-phase droplets, while compound droplet impacts, which are more practically important, received only limited attention. In this work, we experimentally investigate the impact of compound droplets, comprising a water shell and an oil core, on superamphiphobic surfaces. Such core-shell droplets have similar surface tensions but higher viscosities than water and can completely rebound from superamphiphobic surfaces under a wide range of Weber numbers as pure water and oil droplets. However, they show distinct dynamic behaviors due to their different physical properties and energy dissipation processes. The enhanced viscosity due to the oil core strongly dampens surface capillary wave propagation, suppressing air bubble entrapment for droplet impacts at low Weber numbers, but, instead, facilitates the entrapment of a water droplet, resulting in complex water-in-oil-in-water droplet configuration. We demonstrate that such a water entrapment phenomenon provides an alternative strategy for producing submillimeter-sized water-in-oil droplets through the impingement of millimeter-sized oil-in-water droplets on slightly inclined superamphiphobic surfaces. Furthermore, the deformation of the oil-water interface during droplet spreading stores part of the impact energy, and it subsequently serves as an additional source driving droplet recoil, eventually shortening the contact time of all bouncing droplets. These findings offer a better understanding of the droplet impact dynamics of complex fluids and provide guidance for surface engineering and microfluidic device manufacturing. locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon Physics Subject Headings (PhySH)Drop & bubble phenomenaLiquid-solid interfaces