Mixed-metal cyanides (Cu1/2Au1/2)CN, (Ag1/2Au1/2)CN, and (Cu1/3Ag1/3Au1/3)CN adopt an AuCN-type structure in which metal-cyanide chains pack on a hexagonal lattice with metal atoms arranged in sheets. The interactions between and within the metal-cyanide chains are investigated using density functional theory (DFT) calculations, 13C solid-state NMR (SSNMR), and X-ray pair distribution function (PDF) measurements. Long-range metal and cyanide order is found within the chains: (-Cu-NC-Au-CN-)∞, (-Ag-NC-Au-CN-)∞, and (-Cu-NC-Ag-NC-Au-CN-)∞. Although Bragg diffraction studies establish that there is no long-range order between chains, X-ray PDF results show that there is local order between chains. In (Cu1/2Au1/2)CN and (Ag1/2Au1/2)CN, there is a preference for unlike metal atoms occurring as nearest neighbors within the metal sheets. A general mathematical proof shows that the maximum average number of heterometallic nearest-neighbor interactions on a hexagonal lattice with two types of metal atoms is four. Calculated energies of periodic structural models show that those with four unlike nearest neighbors are most favorable. Of these, models in space group Immm give the best fits to the X-ray PDF data out to 8 Å, providing good descriptions of the short- and medium-range structures. This result shows that interactions beyond those of nearest neighbors must be considered when determining the structures of these materials. Such interactions are also important in (Cu1/3Ag1/3Au1/3)CN, leading to the adoption of a structure in Pmm2 containing mixed Cu-Au and Ag-only sheets arranged to maximize the numbers of Cu···Au nearest- and next-nearest-neighbor interactions.