We present a method to obtain quantitative measures of galaxy morphology and apply it to a spectroscopic sample of field galaxies in order to determine the luminosity and stellar mass functions of galactic disks and spheroids. We estimate, for each galaxy, the bulge-to-disk luminosity ratio in the I-band using a two-dimensional image fitting procedure. Monte Carlo simulations indicate that reliable determinations are only possible for galaxies approximately two magnitudes brighter than the photometric completeness limit, leaving a sample of 90 galaxies with well determined bulge-to-total light ratios. We construct the luminosity functions of disks and spheroids and, using a stellar population synthesis model, we estimate the stellar mass functions of each of these components. The disk and spheroid luminosity functions are remarkably similar. We do, however, find evidence in the bi-variate luminosity function that spheroid-dominated galaxies occur only among the brightest spheroids, while disk-dominated galaxies span a much wider range of disk luminosities. Remarkably, the total stellar mass residing in disks and spheroids is approximately the same. For our sample, we find the ratio of stellar masses in disks and spheroids to be 1.3+/-0.2. Ongoing large photometric and redshift surveys will lead to a large increase in the number of galaxies to which our techniques can be applied and thus to an improvement in the current estimates. (abridged)

25 pages, 5 figures, to appear in ApJ