Vibrationally-sensitive spectroscopic techniques are becoming important clinical tools for real-time, in vivo diagnostics. The molecular information made available with these techniques can provide early diagnostic signs of disease, often before morphological changes occur. We model and experimentally demonstrate a new technique for measuring optical spectroscopy signals using interferometric ranging. This new technique, nonlinear interferometric vibrational imaging (NIVI), uses principles from coherent anti-Stokes Raman scattering (CARS) spectroscopy and optical coherence tomography (OCT) to achieve cross-sectional imaging of the distribution of specific molecular species within a sample. Two CARS signals are generated, one from a known reference molecular species and a second from the unknown molecules present in a sample. These coherent signals are interfered with each other using an interferometer setup. The intensity envelope of the interference signal provides a measure of the concentration of selected bonds present in the sample focal volume. The interference fringes themselves can provide phase information that will allow for the exact reconstruction of the vibrational characteristics of the molecules in the sample focal volume. Theoretical background to CARS interferometry is presented, the experimental laser systems are described, and a depth-resolved scan line of a benzene filled cuvette is demonstrated. The experimental results show close resemblance to the theoretical models. The advantages of NIVI over existing vibrational imaging systems and its clinical implications are discussed.