We experimentally investigated the nonlinear optical interaction between the instantaneous four-wave mixing and the cascaded quadratic frequency conversion in commonly used nonlinear optical KTP and LiNbO3 with the aim of a possible background suppression of the non-resonant background in coherent anti-Stokes Raman scattering. The possibility of background-free heterodyne coherent anti-Stokes Raman scattering microspectroscopy is investigated at the interface formed by a liquid (isopropyl alcohol) and a nonlinear crystal (LiNbO3).