Based on the full BABAR data sample, we report improved measurements of the ratios RðDÞ ¼ BðB ! DÞ=BðB ! D‘‘Þ and RðDÞ ¼ BðB ! DÞ=BðB ! D‘‘Þ, where ‘ refers to either an electron or muon. These ratios are sensitive to new physics contributions in the form of a charged Higgs boson. We measureRðDÞ ¼ 0:440 0:058 0:042 and RðDÞ ¼ 0:332 0:024 0:018, which exceed the standard model expectations by 2:0 and 2:7, respectively. Taken together, the results disagree with these expectations at the 3:4 level. This excess cannot be explained by a charged Higgs boson in the type II two-Higgs-doublet model. Kinematic distributions presented here exclude large portions of the more general type III two-Higgs-doublet model, but there are solutions w...