The electron transmission properties of a molecular-electronic switch, represented by a monatomic chain with two atomic impurities, is studied via the tight-binding model. A method, based on the Lippmann-Schwinger equation, is used to obtain simple expressions for the transmission probability. Impurities, occupying neighboring sites in the chain, interact directly and act as a single diatomic impurity. For remote impurities, there is no direct interaction in the tight-binding model, but interference among the multiply reflected Bloch waves between the impurities leads to oscillations in the transmission probability over the energy band. We find that, in either case, controlling the transmission by the impurity-site energies is feasible in the regime of sufficiently weak impurity-chain couplings. \textcopyright{} 1996 The American Physical Society.