We introduce interferometric (I) Fourier-transform (FT) stimulated Raman scattering (SRS) to measure the complex nonlinear vibrational susceptibility of molecules. The technique is a simple variation of FT-SRS, which was previously demonstrated to combine the very high sensitivity of single-channel lock-in detection with the spectral resolution afforded by FT spectroscopy. In IFT-SRS, a local oscillator, temporally anticipated with respect to the broadband pump pulse, enables the interferometric detection of both real and imaginary parts of the nonlinear susceptibility, whose spectrum is recorded in the time domain by scanning the delay of the local oscillator using a birefringent common-path interferometer. We apply IFT-SRS to record the complex vibrational response of different solvents and their mixtures.