We present a detailed morphological, photometric, and kinematic analysis of two barred S0 galaxies with large, luminous inner disks inside their bars. We show that these structures, in addition to being geometrically disk-like, have exponential profiles (scale lengths $∼$ 300--500 pc) distinct from the central, non-exponential bulges. We also find them to be kinematically disk-like. The inner disk in NGC 2787 has a luminosity roughly twice that of the bulge; but in NGC 3945, the inner disk is almost ten times more luminous than the bulge, which itself is extremely small (half-light radius $≈$ 100 pc, in a galaxy with an outer ring of radius $≈$ 14 kpc) and only $∼$ 5% of the total luminosity -- a bulge/total ratio much more typical of an Sc galaxy. We estimate that at least 20% of (barred) S0 galaxies may have similar structures, which means that their bulge/disk ratios may be significantly overestimated. These inner disks dominate the central light of their galaxies; they are at least an order of magnitude larger than typical ``nuclear disks'' found in ellipticals and early-type spirals. Consequently, they must affect the dynamics of the bars in which they reside. Comment: LaTeX, 37 pages, 14 EPS figures. To appear in The Astrophysical Journal (November 10, 2003 issue). Version with full-resolution figures available at http://www.iac.es/galeria/erwin/research/