Coherent anti-Stokes Raman spectroscopy (CARS) uses vibrational resonances to study nuclear wavepacket motions and is widely used in cell imaging and other applications. The resonances usually lie on top of a parametric component that involves no change in the molecular state and creates an undesirable background which reduces the sensitivity of the technique. Here, by examining the process from the perspective of the molecule, rather than the field, we are able to separate the two components and recast each resonance as a modulus square of a transition amplitude which contains an interference between two Stokes pathways, each involving a different pair of field modes. We further propose that dissipative signals obtained by measuring the total absorption of all field modes in a convenient collinear pulse geometry can eliminate the parametric component and retain the purely resonant contributions. Specific vibrational resonances may then be readily detected using pulse shapers through derivatives with respect to pulse parameters.