To uncover the interface proximity effect arising from the interaction between shock wave and near-surface impurity and hole of material in practical applications, a simplified mechanism study on the influence of downstream planar heavy-light interfaces on the evolution of a shock-accelerated heavy gas cylinder was carried out through numerical simulation. The findings reveal that the diffracted and transmitted wave systems formed by the incident shock impacting the heavy gas cylinders successively interact with the downstream planar slow-fast interface, leading to the formation of wave systems that reflect back and forth between the gas cylinder and the downstream planar slow-fast interface. Significantly, these wave systems not only govern the evolution of the gas cylinder interface but also trigger the generation of jets at the downstream planar slow-fast interfaces. Under diverse interfacial spacing conditions, the type of reflected waves originating from the diffracted wave system outside the gas cylinder varies at the downstream interface, and the sequence of the reflected wave system and the focused wave system inside the gas cylinder interacting with the right pole of the gas cylinder is different. When the interfacial distance is narrow, the gas cylinder jet can permeate the gap fluid sandwiched between the gas cylinder and the downstream slow-fast interface and couple with the jet at the downstream planar slow-fast interface, which significantly promotes the evolution of the gas cylinder jet. As the interfacial distance increases, the jet coupling phenomenon progressively wanes, and the gas cylinder jet succumbs to the inhibitory effect of the vortex pair within the gas cylinder. With a further augmentation in interfacial distance, the gas cylinder jet will be promoted by the stretching effect of the reflected rarefaction wave system at the downstream interface. In addition, under different interface spacing conditions, the presence of a downstream planar slow-fast interface invariably augments the development of interfacial width, height, as well as circulation deposition.