This paper studies the process of mutual neutralization of Si^+ and H^- ions in slow collisions within the multichannel Landau-Zener model. All important ionic-covalent couplings in this collision system are included in the collision dynamics. The cross sections for population of specific final states of product Si atom are calculated in the CM energy range 0.05 e∨/u-5 ke∨/u. Both singlet and triplet states are considered. At collision energies below -10 e∨/u, the most populated singlet state is Si(3p4p, ^1S0), while for energies above -150e∨/u it is the Si(3p, 4p, ^1P1) state. In the case of triplet states, the mixed 3p4p(^3S1 +^3P0) states are the most populated in the entire collision energy range investigated. The total cross section exhibits a broad maximum around 200 300e∨/u and for ECM ≤ 10e∨/u it monotonically increases with decreasing the collision energy, reaching a value of 8 × 10^-13 cm^2 at ECM = 0.05 e∨/u. The ion-pair formation process in Si(3p^2 ^3PJ)+H(1s) collisions has also been considered and its cross section in the considered energy range is very small (smaller than 10^-20 cm^2 in the energy region below 1 ke∨/u).