We address the general problem of detecting chemical interfaces arbitrarily oriented in space in coherent anti- Stokes Raman scattering (CARS) microscopy. Such a task is accomplished by using a beam reversal scheme, as recently demonstrated experimentally [J. Biomed. Opt. 16, 086006 (2011)]. We develop a full vectorial theoretical analysis of the situation and show that transverse chemical interfaces are readily highlighted without special care in the CARS signal detection. In addition, a finer analysis reveals that adequate angular analysis of the CARS far-field radiation pattern enables the detection of axial interfaces. Background-free CARS microscopy and spectroscopy are thus achievable through the combined application of excitation beam reversal and angular analysis of the CARS far-field radiation pattern. This differential CARS (D-CARS) technique is relevant for fast detection of interfaces between molecularly different media.