Photometric bulge-disk decompositions are often used as a way to separate out galaxies into their individual components. In order to assess whether the structural components obtained by performing such decompositions correspond to distinct stellar components, we have developed a technique to decompose spectral data cubes into such elements, solving separately for the stellar kinematics and populations that make up each of the components, but constrained to match the overall broadband photometric decomposition. An initial application of this method to the CALIFA integral field unit observations of three isolated S0 galaxies confirms that they can be physically and robustly decomposed into a rotating dispersion-dominated, bulge component and a rotating, low-dispersion disk component. Analysis of the resulting stellar populations show that the bulges of these galaxies are systematically older than their disks, consistent with them being the result of spiral galaxies whose star formation has ceased as they ran out of gas. This test case indicates the broad potential for extracting individual galaxy components from spectral data cubes, and for using such decompositions to understand the interplay between these various components, and hence how such systems formed.