Comprehensive calculations were performed to predict the phase behavior of large spherical colloids mixed with small spherical colloids that act as a depletant. To this end, the free volume theory (FVT) of Lekkerkerker et al. [Europhys. Lett. 20, 559 (1992)] is used as a basis and is extended to explicitly include the hard-sphere character of colloidal depletants into the expression for the free volume fraction. Taking the excluded volume of the depletants into account in both the system and the reservoir provides a relation between the depletant concentration in the reservoir and that in the system that accurately matches with computer simulation results of Dijkstra et al. [Phys. Rev. E 59, 5744 (1999)]. Moreover, the phase diagrams for highly asymmetric mixtures with size ratios q ⪍ 0.2 obtained by using this new approach corroborate simulation results significantly better than earlier FVT applications to binary hard-sphere mixtures. The phase diagram of a binary hard-sphere mixture with a size ratio of q = 0.4, where a binary interstitial solid solution is formed at high densities, is investigated using a numerical free volume approach. At this size ratio, the obtained phase diagram is qualitatively different from previous FVT approaches for hard-sphere and penetrable depletants but again compares well with simulation predictions.