We propose and test a method of simultaneously characterizing ultrashort laser pulses and the nonlinear susceptibility of the irradiated medium at the site where nonlinear interactions occur. In this method, a coherent anti-Stoke Raman scattering (CARS) spectrogram is generated with the hybrid CARS technique. We confirm that abundant information is contained in, and can be extracted from, this spectrogram and develop an extraction algorithm. With this method, quantitative and comparable broadband CARS imaging based on phase retrieval is achievable without a second material for nonresonant background generation. Furthermore, this method also paves the way for studying highly localized nonlinear light-matter interactions.