We demonstrate synthesis of a new type of heterostructures that comprise two-dimensional (2D) nanosheets (NSs) epitaxially grown at one-dimensional (1D) nanowires (NWs). The synthesis involves materials with a graphite-like layered structure in which covalently bonded layers are held by weak van der Waals forces. GeS was used as a prototype material in this work. The synthesis also involves a seeded-growth process, where GeS NWs are grown first as seeds followed by a seeded growth of NSs at the pre-grown NWs. We observe that exposing the pre-grown NWs to air prior to the seeded growth is critical for the formation of NSs to yield NS-NW heterostructures. Our experimental results suggest that this might be due to a mild oxidation at the NW surface caused by the air exposure, which could subsequently facilitate the nucleation of NSs at the NWs. It also suggests that the surface oxidation needs to be controlled in a proper range in order to achieve optimized NS growths. We believe that this synthetic strategy may generally apply to the growth of NS-NW heterostructures of other layered chalcogenide materials. NS-NW heterostructures provide capabilities to monolithically integrate the functionality of 1D NWs and 2D NSs into a 3D space. It holds great potential in applications that request complex nanomaterials with multiple functionality, high surface area, and efficient charge transport, such as energy storage, chemical sensing, solar energy conversion, and 3D electric and photonic devices.