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Thin films of functional materials, from graphene to semiconductor heterostructures, and from nanomembranes to Langmuir-Blodgett films play key roles in modern technologies. For such films optical interrogation is the main and often the only practical method of characterization. Here, we show that characterization of the optical response of thin films can be greatly improved with a type of coherent spectroscopy using two counterpropagating beams of light. The spectroscopy is selective to particular types of multipole resonances that form the absorption spectrum of the film, and therefore can reveal lines that are hidden in conventional absorption spectroscopy. We explicitly demonstrate selectivity of this spectroscopy in a series of proof-of-principle experiments with plasmonic metamaterial arrays designed to exhibit different multipole resonances. We further demonstrate the analytic potential of this spectroscopy by …