Selective non-covalent interactions have been widely exploited in solution-based chemistry to direct the assembly of molecules into nanometre-sized functional structures such as capsules, switches and prototype machines. More recently, the concepts of supramolecular organization have also been applied to two-dimensional assemblies on surfaces stabilized by hydrogen bonding, dipolar coupling or metal co-ordination. Structures realized to date include isolated rows, clusters and extended networks, as well as more complex multi-component arrangements. Another approach to controlling surface structures uses adsorbed molecular monolayers to create preferential binding sites that accommodate individual target molecules. Here we combine these approaches, by using hydrogen bonding to guide the assembly of two types of molecules into a two-dimensional open honeycomb network that then controls and templates new surface phases formed by subsequently deposited fullerene molecules. We find that the open network acts as a two-dimensional array of large pores of sufficient capacity to accommodate several large guest molecules, with the network itself also serving as a template for the formation of a fullerene layer.