Although there have been great advances in understanding the effect of cholesterol on various properties of lipid membranes, its mechanistic role in determining the elasticity of bilayers at the molecular level is not fully resolved. Indeed, to date the molecular mechanisms that drive the experimentally detected differences in properties of saturated and unsaturated lipid bilayers that contain cholesterol remain unclear. By quantifying the cholesterol orientational degrees of freedom from atomistic molecular dynamics simulations of mixed lipid-cholesterol membranes, we address this question from the perspective of cholesterol tilt and splay. Following the fluctuations in orientations of cholesterol and of lipid molecules in simulations, we have extracted tilt and splay moduli both for cholesterol molecules and hydrocarbon lipid tails. This has further allowed us to estimate the contributions of these modes to the response of membranes to elastic deformations. We find that tilt and splay deformations importantly contribute to the overall elasticity of the mixed lipid membranes, and that they can account for the experimentally established differences between the liquid ordered sphingomyelin (SM)/cholesterol bilayers and fluid dioleoylphosphocholine (DOPC)/cholesterol bilayers. These findings underscore the importance of tilt and splay moduli, derived from simulations with relative computational ease, as useful metrics for quantitatively characterizing the mechanical properties of mixed lipid-cholesterol bilayers.