A theoretical approach to calculate the correlation functions in binary hard-sphere (HS) solid mixtures is developed. The method is motivated by the theory of correlations in one-component HS solids [Rascon et al., Phys. Rev. E 54, 1261 (1996)] and the Kirkwood-Buff theory for solutions. Combined with the fundamental measure density functional theory the approach provides correlation functions in good agreement with the numerical simulations results for the moderately asymmetric mixtures.