A self-consistent model is presented for the simulation of a multi-component plasma in the tokamak boundary. A deuterium plasma is considered, with the plasma species that include electrons, deuterium atomic ions and deuterium molecular ions, while the deuterium atoms and molecules constitute the neutral species. The plasma and neutral models are coupled via a number of collisional interactions, which include dissociation, ionization, charge-exchange and recombination processes. The derivation of the three-fluid drift-reduced Braginskii equations used to describe the turbulent plasma dynamics is presented, including its boundary conditions. The kinetic advection equations for the neutral species are also derived, and their numerical implementation discussed. The first results of multi-component plasma simulations carried out by using the global Braginskii solver (GBS) code are then presented and analyzed, being compared with results obtained with the single-component plasma model.