We report a new approach to characterization of thin (bio)molecular films based on spectroscopy of Bragg-scattered surface plasmons (BSSPs) generated by diffraction-coupling of counterpropagating surface plasmons on a metal-coated diffraction grating. The BSSPs exhibit fields with different penetration depths into the medium adjacent to the metal and therefore exhibit unequal sensitivities to the presence of (bio)molecular films on the surface of the metal. Therefore, spectroscopy of BSSPs enables in situ observation of the formation of biomolecular films and determination of both their refractive index and thickness. We demonstrate this capacity of spectroscopy of BSSPs in a model experiment in which growth of protein layers on a gold surface is studied.