This work is devoted to the analysis of the shape of transmission spectra of composite systems including a thin adsorbed layer of absorbing dye molecules. It is demonstrated, that different from the often observed absorption characteristics in the transmission spectra as determined by the imaginary part of the layer's dielectric function, the transmission spectra are in general determined by coherent light scattering of the molecules in the layer and an interference of this scattered light with the incident light. As a result, the shape of the dispersion of both, imaginary and real parts of the layer's dielectric function, determines the transmission spectrum. Such spectra cannot be constructed from the transmission spectra of the initial system and the deposited film alone. It is shown that the shape of the transmission spectra of the composite films is described in general by an asymmetrical line like a Fano line and that the origin of such a shape can be associated with the physics underlying a Fano resonance. It is shown experimentally and theoretically that the deposition of a thin absorbing layer can give rise to an increase in the transmission of an initial system.