The impact of droplets on liquid films is a ubiquitous phenomenon not only in nature but also in many industrial applications. Compared to the widely-studied impact of droplets on films of identical fluids, the impact of droplets on immiscible films has received far less attention. In the present work, we show using high-speed imaging that immiscibility has a profound effect on the impact dynamics. The impact of a water droplet on an oil film leads to the formation of a compound crown followed by a central jet, whereas that of an oil droplet on a water film results in rapid spreading on the film surface driven by a large, positive spreading factor. In the former scenario, the central jet occurs due to the severe stretching of the droplet during the formation of the crown and then the retraction of the droplet by capillarity, which leads to the collision of fluid at the impact point. A model for the elongation dynamics of the central jet is proposed based on energy conservation. The effects of key parameters controlling the impact process are analysed, including the droplet Ohnesorge and Weber numbers, the viscosity ratio, and the dimensionless film thickness. Different impact outcomes are discussed, such as bouncing, deposition, and oscillation of the impact droplet, the formation and collapse of the compound crown, and the formation and tip-pinching of the central jet. This study not only provides physical insights into the impact dynamics, but could also facilitate the control and optimisation of the droplet impact process in a number of applications as highlighted herein.