A theoretical formalism for the interpretation of scanning-tunneling- microscopy (STM) images is developed with special attention to the effects of adsorbate molecules placed in the tip-substrate gap. The STM configuration is treated as a system of three groups of states, the substrate, the adsorbate, and the tip, in contact with a thermal reservoir, with which it exchanges energy as well as particles. The calculation of the observed current is approached as a transport problem in quantum statistical mechanics with focus on the description of the arbitrary degree of quantum coherence in the tunnel junction and of the temperature and complexity of the adsorbate. Expressions are obtained for the STM current and for the effective resistance of the STM junction. They are shown to allow one to relax some of the restrictive assumptions made in existing approaches. Particular cases are worked out, observable quantum interference effects are predicted, and simple examples suggesting the nature of the mechanism of contrast of adsorbed molecules are presented along with the corresponding images. © 1995 The American Physical Society.