  In the "Higgs basis" for a generic 2HDM, only one doublet gets a nonzero
vacuum expectation value and, under the criterion of minimal flavour violation,
the other one is fixed to be either colour-singlet or colour-octet, referred
respectively as the type-III and the type-C model. Both of them can naturally
avoid large FCNC transitions and provide very interesting phenomena in some
low-energy processes. In this paper, we study their effects on exclusive
radiative B-meson decays due to the exchange of colourless or coloured charged
Higgs. It is found that, while constraints from the branching ratios are
slightly weaker than the ones from the inclusive $B\to X_{s} \gamma$ decay, the
isospin asymmetries in exclusive decays provide very complementary bounds on
the model parameters. As the two models predict similar corrections to the
dipole coefficient $C_7^{\rm eff}$ whereas similar magnitudes but with opposite
signs to $C_8^{\rm eff}$, the branching ratios cannot discriminate the two
models, and we have to resort to the direct CP and isospin asymmetries of $b\to
s$ processes, which are more sensitive to $C_8^{\rm eff}$. Due to the CKM
factors $|\lambda_u^{(d)}|\sim|\lambda_t^{(d)}|$, the terms proportional to
$\lambda_u^{(d)}$ make the observables of $b\to d$ processes exhibit a
different dependence on the possible new physics phase. In addition,
correlations between the various observables in the exclusive $B\to V\gamma$
and the inclusive $B\to X_{s,d}\gamma$ decays are investigated, which could
provide further insights into the models with more precise experimental
measurements and theoretical predictions for these decays.
