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A new method is proposed to analyze doubly-resonant infrared-visible sum-frequency (DR-SFG) spectra. Based on the transform technique, this approach is free from assumptions about vibronic modes, energies, or line widths, and accurately captures through the overlap spectral function all required aspects of the vibronic structure from simple experimental linear absorption spectra. Details and implementation of the method are provided, along with three examples treating rhodamine thin films about one monolayer thick. The technique leads to a perfect agreement between experiment and simulations of the visible DR-SFG lineshapes, even in the case of complex intermolecular interactions resulting from J-aggregated chromophores in heterogeneous films. For films with mixed H-and J-aggregates, separation of their responses shows that the J-aggregate DR-SFG response is dominant. Our analysis also accounts for the unexplained results published in the early times of DR-SFG experiments.