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 disklike, have exponential profiles (scale lengths ~300-500 pc) distinct from the central, nonexponential bulges. We also find them to be kinematically disklike. The inner disk in NGC 2787 has a luminosity roughly twice that of the bulge; but in NGC 3945, the inner disk is almost 10 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 has 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 elliptical and early-type spiral galaxies. Consequently, they must affect the dynamics of the bars in which they reside.