In this paper we study excluded volume interactions, the free volume fraction available, and the phase behaviour, in mixtures of hard spheres (HS) and hard rods, modeled as spherocylinders. We use free volume theory (FVT) to predict various physical properties and compare to Monte Carlo computer simulations. FVT is used at two levels. We use the original FVT approach in which it is assumed that the correlations of the HS are not affected by the rods. This is compared to a recent, more rigorous, FVT approach which includes excluded volume interactions between the different components at all levels. We find that the novel rigorous FVT approach agrees well with computer simulation results at the level of free volume available, as well as for the phase stability. The FVT predictions show significant quantitative and qualitative deviations with respect to the original FVT approach. The phase transition curves are systematically at higher rod concentrations than previously predicted. Furthermore, the calculations revealed that a certain asphericity is required to induce isostructural fluid-fluid coexistence and the stability region is highly dependent on the size ratio between the rods and the spheres.