We present a purely optical method for background suppression in nonlinear spectroscopy based on linear interferometry. Employing an unbalanced Sagnac interferometer, an unprecedented background reduction of 17 dB over a broad bandwidth of 60 THz (2000 cm(-1)) is achieved and its application to femtosecond stimulated Raman scattering loss spectroscopy is demonstrated. Apart from raising the signal-to-background ratio in the measurement of the Raman intensity spectrum, this interferometric method grants access to the spectral phase of the resonant χ(3) contribution. The spectral phase becomes apparent as a dispersive lineshape and is reproduced numerically with a simple oscillator model.