We present the QCD corrections to R b and to the ∆B = 1 effective Hamiltonian in models with a second Higgs field that couples to the quarks respecting the criterion of Minimal Flavor Violation, thus belonging either to the (1, 2) 1/2 or to the (8, 2) 1/2 representation of SU (3) × SU (2) × U (1). After the inclusion of the QCD corrections, the prediction for R b becomes practically insensitive to the choice of renormalization scheme for the top mass, which for the type-I and type-II models translates in a more robust lower bound on tan β. The QCD-corrected determinations of R b and BR(B → X s γ) are used to discuss the constraints on the couplings of a (colored) charged Higgs boson to top and bottom quarks.