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We compute three-loop matching corrections to the Wilson coefficients $C_7$and $C_8$ in the Two Higgs Doublet Model by applying expansions for small,intermediate and large charged Higgs boson masses. The results are used toevaluate the branching ratio of $\bar{B}\to X_s \gamma$ to next-to-next-toleading order accuracy, and to determine an updated lower limit on the chargedHiggs boson mass. We find $\mhplus \ge 380 $GeV at 95% confidence level whenthe recently completed BABAR data analysis is taken into account. Our resultsfor the charged Higgs contribution to the branching ratio exhibit considerablyweaker sensitivity to the matching scale $\mu_0$, as compared to previouscalculations.

$\bar{B}\to X_s \gamma$ in the Two Higgs Doublet Model up to Next-to-Next-to-Leading Order in QCD