Angular distributions of electrons scattered elastically and inelastically from cold solid molecular films of ethylene and nitrogen in various proportions, grown from the gas phase at different temperatures, have been studied by high-resolution electron energy loss spectroscopy. The probing depth of dipole and impact scattering has been investigated by covering the sample by overlayers of argon of increasing thickness. The angular distribution measured for elastically and inelastically dipole-scattered electrons was found to be peaked about the specular direction for all surface conditions studied, while a diffuse angular distribution was possible for electrons that underwent dipole-forbidden scattering. These results allow us to identify favorable conditions for monitoring the composition of a solid sample during the course of reactions occurring under exposure to low-energy electrons.