  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)xSU(2)xU(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 Rb and BR(B->Xs gamma) are used
to discuss the constraints on the couplings of a (colored) charged Higgs boson
to top and bottom quarks.
