Multispectral LiDAR enables joint observations of the 3D geometry and material properties of natural targets by combining ToF-based distance measurements with remote spectroscopy. Established multispectral LiDAR solutions provide mm-level range resolution and reflectance estimates of the target material over some tens of spectral channels. We propose a novel multispectral LiDAR approach based on an ultra-broadband frequency comb that enables enhanced remote spectroscopy by resolving relative delays in addition to reflectance. The spectrally-resolved delay and power measurements are transformed into distance and reflectance spectra by differential observations to a common reference object and adequate system calibration. These distance and reflectance spectra encode material information related to the surface and sub-surface composition and small-scale geometry. We develop the proposed comb-based multispectral LiDAR on an implementation covering the spectral range between 580 nm and 900 nm on 2 different spectral configurations with 7 and 33 channels of different spectral width. The performance assessment of the implemented system demonstrates a distance measurement precision better than 0.1 mm on most channels. Table-top probing results on five material specimens show that both the distance and the reflectance spectra alone enable discrimination of material specimens, while the novel distance signature particularly complements reflectance and increases classification accuracy when the material surface exhibits significant reflectance inhomogeneity. Material classification results using a support vector machine with radial basis function kernel demonstrate the potential of this approach for enhanced material classification by combining both signature dimensions.