  We assume that the 125 GeV Higgs discovered at the LHC is the heavy CP-even
Higgs of the two-Higgs-doublet models, and examine the parameter space in the
Type-I, Type-II, Lepton-specific and Flipped models allowed by the latest Higgs
signal data, the relevant experimental and theoretical constraints. Further, we
show the projected limits on $\tan\beta$, $\sin(\beta-\alpha)$, $Hf\bar{f}$ and
$HVV$ couplings from the future measurements of the 125 GeV Higgs at the LHC
and ILC, including the LHC with integrated luminosity of 300 fb$^{-1}$ (LHC-300
fb$^{-1}$) and 3000 fb$^{-1}$ (LHC-3000 fb$^{-1}$) as well as the ILC at
$\sqrt{s}=250$ GeV (ILC-250 GeV), $\sqrt{s}=500$ GeV (ILC-500 GeV) and
$\sqrt{s}=1000$ GeV (ILC-1000 GeV). Assuming that the future Higgs signal data
have no deviation from the SM expectation, the LHC-300 fb$^{-1}$, LHC-3000
fb$^{-1}$ and ILC-1000 GeV can exclude the wrong-sign Yukawa coupling regions
of the Type-II, Flipped and Lepton-specific models at the $2\sigma$ level,
respectively. The future experiments at the LHC and ILC will constrain the
Higgs couplings to be very close to SM values, especially for the $HVV$
coupling.
