A stable hydrogen-bonding junction is formed between 3,4,9,10-perylene-3,4,9,10-tetracarboxylic-dianhydride (PTCDA) and 1,3,5-triazine-2,4,6-triamine (melamine). This bimolecular system was studied on the Ag-Si(111) square root 3 x square root R 30 degrees surface at sub-monolayer coverage, and two distinct phases are observed. A hexagonal lattice is formed that is stabilized by hydrogen bonding between PTCDA and melamine. This phase, in which melamine acts as a 3-fold vertex, is a close analogue to the 3,4,9,10-perylene-3,4,9,10-tetracarboxylic-diimide-melamine network reported recently. To our knowledge this hydrogen-bonding junction has not been previously observed and might not be expected due to lone pair repulsion. However we confirm that this combination is stable using ab initio methods. In the second intermixed phase parallel rows of PTCDA molecules coexist with an array of melamine molecules, and we propose a model for this structure.