A sodium chloride monolayer on a Cu(110) surface gives rise to a highly corrugated periodic nanostripe pattern of the (100) lattice as observed by scanning tunneling microscopy and low-energy electron diffraction. As revealed by density-functional calculations, this pattern is a consequence of the frustration of the overlayer-substrate chemical bonding produced by epitaxial mismatch. The coexistence of regions of strong Cu-Cl covalent and weak nonbonding interactions leads to a chemically induced topographic modulation here realized in a two-dimensional dielectric. The carpetlike growth of the NaCl layer across Cu step edges induces a distinct contrast inversion in the stripe pattern as a result of the change in epitaxial relationship due to the stacking sequence of the (110) Cu layers. It is demonstrated that the competition between local substrate-overlayer and intraoverlayer interactions can support a well-defined heteroepitaxial relationship of a ionic dielectric film and a metal surface, with important consequences for the nanoscale morphology and related properties.