We have studied the transmission of low energy (<10 eV) O-16(+) ions through ultrathin films of condensed molecular solids, NH3 and (H2O)-O-18, in order to address the fundamental scattering processes that occur in the desorption of ions from below the surface of solids. O-16(+) ions with a peak energy of similar to 7 eV and a narrow angular distribution [full-width at half-maximum (FWHM) similar to 15 degrees] are generated by means of electron stimulated desorption (ESD) from an O-16 oxidized W(100) surface and their yield, energy and angular distribution are measured with a digital ESDIAD (ESD ion angular distribution) detector. Ultrathin NH3 and (H2O)-O-18 films of known thickness are condensed on the oxidized surface at 25 K and changes in the ion yield, energy and angular distribution are observed as a function of coverage. We find that adsorption of only 0.5 monolayer of (H2O)-O-18 is enough to suppress the O-16(+) ion emission by a factor of 100, while three monolayers of NH3 are necessary for equivalent suppression of the O-16(+) ion emission. The angular distribution of the ions increases slightly with increasing overlayer coverage. We also fmd that a small percentage of (H2O)-O-18 dissociates upon adsorption. We suggest that one electron charge transfer between O-16(+) and (H2O)-O-18, and between O-16(+) and the dissociation product OH are the main reasons for the strong attenuation of O-16(+) ions by only a fraction of a monolayer of (H2O)-O-18. Charge transfer is also believed to be the main process that causes suppression of O-16(+) ions by ultrathin NH3 films. Other elastic and inelastic processes are not believed to contribute significantly to O-16(+) attenuation in NH3 or (H2O)-O-18 films.