We report a theoretical description and experimental implementation of multiplex coherent anti-Stokes Raman scattering (M-CARS) microspectroscopy using a picosecond pump beam and a femtosecond Stokes beam. The effect of the chirp in the Stokes pulse on a M-CARS spectrum is studied. Polarization-sensitive detection is utilized for suppression of the nonresonant background and for selective detection of spectrally overlapped Raman bands. M-CARS spectra of liposomes in the C-H stretching vibration region were acquired. Polarization CARS imaging of lipids in live cells based on the M-CARS spectra is demonstrated.