The spontaneous organization of multicomponent micrometre-sized colloids or nanocrystals into superlattices is of scientific importance for understanding the assembly process on the nanometre scale and is of great interest for bottom-up fabrication of functional devices. In particular, co-assembly of two types of nanocrystal into binary nanocrystal superlattices (BNSLs) has recently attracted significant attention, as this provides a low-cost, programmable way to design metamaterials with precisely controlled properties that arise from the organization and interactions of the constituent nanocrystal components. Although challenging, the ability to grow and manipulate large-scale BNSLs is critical for extensive exploration of this new class of material. Here we report a general method of growing centimetre-scale, uniform membranes of BNSLs that can readily be transferred to arbitrary substrates. Our method is based on the liquid-air interfacial assembly of multicomponent nanocrystals and circumvents the limitations associated with the current assembly strategies, allowing integration of BNSLs on any substrate for the fabrication of nanocrystal-based devices. We demonstrate the construction of magnetoresistive devices by incorporating large-area (1.5 mm x 2.5 mm) BNSL membranes; their magnetotransport measurements clearly show that device magnetoresistance is dependent on the structure (stoichiometry) of the BNSLs. The ability to transfer BNSLs also allows the construction of free-standing membranes and other complex architectures that have not been accessible previously.