The modification of the Ornstein-Zernike (OZ) equation for mixtures is derived and numerically solved for binary mixtures of hard spheres (HS) or hard spheres and hard prolate spherocylinders (HPS) with length-to-breadth ratio gamma = 2.0. The solution method results in average pair correlation functions. To test the proposed theoretical approach, Monte Carlo (MC) simulations in NVT ensemble are employed. The HS binary systems with diameter ratios 0.4 and 0.7 and HS + HPS mixtures with spherocylinder thicknesses 1, 0.4, and 0.3 of sphere diameter were simulated, and the average correlation functions plus compressibility factors of studied mixtures are listed. The theoretical prediction of average correlation functions generally agrees well with the MC data, however, for some of the studied systems, the results are not so satisfactory.