The charge- and atom-transfer reactions between Br+, HBr+, and DBr+ ions and HBr and DBr molecules have been studied in a HBr + DBr + He free jet. The ionic reactants in specific internal states were prepared by resonance multiphoton ionization of either HBr or DBr, and the ionic products were analyzed by mass spectrometry. A set of eight energetically possible reactions was considered in each case, including ions born in near-resonant ionization and photodissociation processes. Kinetic equations were integrated numerically over the appropriate reaction time and an optimization problem was solved to determine rate coefficients fit to final fractions of all ions measured in an experiment. Analytical expressions for the final fractions also were obtained and were used to derive the rate coefficients more accurately. The work is an example of a multireaction study without direct observation of all the reaction products.