We report an angle-tilted, wavelength-multiplexed ptychographic modulation approach for multispectral lensless on-chip microscopy. In this approach, we illuminate the specimen with lights at five wavelengths simultaneously. A prism is added at the illumination path for spectral dispersion. Thus, lightwaves at different wavelengths hit the specimen at slightly different incident angles, breaking the ambiguities in mixed-state ptychographic reconstruction. At the detection path, we place a thin diffuser between the specimen and the monochromatic image sensor for encoding the spectral information into 2D intensity measurements. By scanning the sample to different x-y positions, we acquire a sequence of monochromatic images for reconstructing the five complex object profiles at the five wavelengths. An up-sampling procedure is integrated into the recovery process to bypass the resolution limit imposed by the imager pixel size. We demonstrate a half-pitch resolution of 0.55 µm using an image sensor with 1.85 µm pixel size. We also demonstrate quantitative and high-quality multispectral reconstructions of stained tissue sections for digital pathology applications.