Thick disks are faint and extended stellar components found around several disk galaxies including our Milky Way. The Milky Way thick disk, the only one studied in detail, contains mostly old disk stars (≈10 Gyr), so that thick disks are likely to trace the early stages of disk evolution. Previous detections of thick disk stellar light in external galaxies have been originally made for early-type, edge-on galaxies but detailed 2D thick/thin disk decompositions have been reported for only a scant handful of mostly late-type disk galaxies. We present in this paper for the first time explicit 3D thick/thin disk decompositions characterising the presence and properties (e.g. scalelength and scaleheight) for a sample of eight lenticular galaxies by fitting 3D disk models to the data. For six out of the eight galaxies we were able to derive a consistent thin/thick disk model. The mean scaleheight of the thick disk is 3.6 times larger than that of the thin disk. The scalelength of the thick disk is about twice, and its central luminosity density between 3-10% of, the thin disk value. Both thin and thick disk are truncated at similar radii. This implies that thick disks extend over fewer scalelengths than thin disks, and turning a thin disk into a thick one requires therefore vertical but little radial heating. All these structural parameters are similar to thick disk parameters for later Hubble-type galaxies previously studied. We discuss our data in respect to present models for the origin of thick disks, either as pre- or post-thin-disk structures, providing new observational constraints. Based on observations obtained at the European Southern Observatory, Chile. Full appendices are only available in electronic form at http://www.edpsciences.org