Neutral aqueous zinc-air batteries (ZABs) are an emerging type of energy devices with substantially elongated lifetime and improved recyclability compared to conventional alkaline ZABs. However, their development is impeded by the lack of robust bifunctional catalyst at the air-electrode for the oxygen evolution reaction (OER) and the oxygen reduction reaction (ORR). Here, we report the controlled synthesis of NiFe2O4/FeNi2S4 heterostructured nanosheets (HNSs) that are highly efficient in catalyzing OER and ORR, therefore enabling neutral rechargeable ZABs. Associated with the formation of abundant oxide/sulfide interfaces over NiFe2O4/FeNi2S4 HNSs' surfaces, the catalyst's oxygen binding energy can be effectively tuned to enhance the OER and ORR activities, as revealed by the density functional theory calculations. In 0.2 M phosphate buffer solution, the optimized NiFe2O4/FeNi2S4 HNSs present an excellent oxygen electrocatalytic activity and stability, with much lower OER and ORR overpotentials than single-component FeNi2S4 or NiFe2O4 and with negligible performance decay in accelerated durability testing. When used as an air-electrode, the NiFe2O4/FeNi2S4 HNSs can deliver a power density of 44.4 mW cm-2 and a superior cycling stability (only 0.6% decay after 900 cycles at 0.5 mA cm-2), making the resultant ZAB the most efficient and robust one with a neutral aqueous electrolyte reported to date. This work highlights the essential function of the heterostructure interface in oxygen electrocatalysis, opening a new avenue to advanced neutral metal-air batteries.