Ultrathin well-ordered films of KBr on NaCl (100) and of NaCl on KBr (100) have been grown. The films were imaged by means of noncontact atomic force microscopy with atomic resolution under ultrahigh vacuum conditions. An extreme asymmetry in the structure of the interface was found for the two systems. The first layer of KBr on NaCl (100) grows with the lattice constant of bulk KBr, while the first layer of NaCl on KBr (100) stretches to the bulk lattice constant of KBr. The KBr films exhibit a superstructure with the periodicity of the least common multiple of the NaCl and KBr lattice constants, while the stretched NaCl films grow flat. We discuss the anharmonicity of the ionic bond as origin of the dependence of the interface structure on the growth sequence.