Imposing the theoretical constraints from vacuum stability, unitarity and perturbativity as well as the experimental constraints from the electroweak precision data, flavor observables and the non-observation of additional Higgs at collider, we study the implications of available Higgs signals on a two-Higgs-doublet model with the alignment of the down-type quarks and charged lepton Yukawa coupling matrices. Compared to the four traditional types of two-Higgs-doublet models, the model has two additional mixing angles θd and θl in the down-type quark and charged lepton Yukawa interactions. We find that the mixing angle θd can loose the constraints on sin(β − α), tan β and mH ± sizably. The model can provide the marginally better fit to available Higgs signals data than SM, which requires the Higgs couplings with gauge bosons, \documentclass[12pt]{minimal}
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\begin{document}$ d\overline{d} $\end{document} to be properly suppressed, and favors (1 < θd< 2, 0.5 < θl< 2.2) for mh = 125.5 GeV and (0.5 < θd< 2, 0.5 < θl< 2.2) for mH = 125.5 GeV. However, these Higgs couplings are allowed to have sizable deviations from SM for (mh = 125.5 GeV, 125.5 ≤ mH ≤ 128 GeV) and (125 GeV ≤ mh ≤ 125.5 GeV, mH = 125.5 GeV).