We present the QCD corrections to R(b) and to the Delta 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) x SU(2) x 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 beta. The QCD-corrected determinations of R(b) and BR(B -> X(s)gamma) are used to discuss the constraints on the couplings of a (colored) charged Higgs boson to top and bottom quarks.