Stimulated Raman scattering (SRS) allows chemical identification of substances based on their third-order nonlinear vibrational susceptibility χ(3)(ω). In its standard single-frequency implementation, SRS can only access the imaginary part of χ(3)(ω). Here we introduce interferometric SRS (iSRS), which has the capability to measure both the real and the imaginary parts of the nonlinear susceptibility. With respect to a standard SRS setup, iSRS simply requires the insertion of a few optical elements in the Stokes(pump) beam pathway to generate an intrinsically phase-coherent local oscillator. While preserving the acquisition speed and the simplicity of single-frequency SRS, iSRS considerably increases its information content by providing access to the vibrational phase, which allows one to distinguish overlapping species in congested spectra and is more robust with respect to noise.