We present a detailed study of 3,4,9,10-perylene-and 1,4,5,8-naphthalene-tetracarboxylic acid dianhydride monolayers adsorbed on Ag(111) film. The study is based on density functional theory with the use of a periodic slab model. The slab is chosen to contain an organic molecular monolayer on a silver thin film of different thicknesses (6, 9, and 12 layers) with the (111) orientation. We show that in both cases there is a similarity in formation of an unoccupied interface state from a surface state of the bare Ag(111) film due to the adsorbate-substrate interaction. The energy difference between the initial surface state and the resulting interface state varies with the film thickness, the adsorption distance, and the molecule size and geometry, whereas the effective mass of the state remains practically unchanged. Also, we demonstrate that the interface-state charge distribution preserves its localization in the interface region at different wave vectors k and in the vicinity of the molecular plane resembles lowest unoccupied orbitals of free molecules.