The authors present a comprehensive method of spectral reflectance estimation for points sampled on a 3D surface in a structured-light projection system. The proposed solution does not require any additional hardware apart from the devices used in the classic structured-light projection setup. It utilizes a calibrated color CCD camera and a DLP projector, which projects sine fringes in order to provide precise 3D point coordinates. Additionally, the projector is used as a light source for multispectral image capture by displaying uniform color fields. Two approaches are verified for the design of optimal projected hues. Simultaneous acquisition of the 3D shape information as well as the multispectral data is possible in a single sequence of images. They are corrected for illumination nonuniformity, ambient light and camera noise. The presented method reconstructs a point cloud representing the surface with spectral reflectance estimated for each point. It uses the Wiener inverse method for spectrum reconstruction. The authors provide an evaluation of the accuracy of the proposed method and show the results of scanning painting samples created with different techniques, as an example application of cultural heritage digitization.