Polarimetric LiDAR combines polarimetry and non-coherent optical ranging techniques to complement the acquisition of geometrical information with material characteristics. In recent decades, polarimetric LiDAR has been widely explored in material probing, target detection, and object identification. These approaches have so far mainly relied on implementations using a single or very few wavelengths. In this work, we propose, develop and evaluate a polarimetric femtosecond-laser LiDAR that enables extracting multispectral polarization signatures on 7 spectral channels of 40 nm spectral bandwidth and 33 spectral channels of 10 nm spectral bandwidth in the visible and near-infrared range. Multispectral polarization signatures of five material specimens (cardboard, foam, plaster, plastic, and wood board) are obtained and used as input features on a linear support vector machine classification algorithm. The results show that extending polarimetric probing to multiple spectral channels improves the classification capabilities with respect to single-wavelength approaches. The combination of different spectral signature dimensions (polarization, reflectance, and distance) that can be derived from Li-DAR measurements is also analyzed, with results indicating their capability to support challenging classification tasks.