  We consider the two-Higgs-doublet model as a framework in which to evaluate
the viability of scenarios in which the sign of the coupling of the observed
Higgs boson to down-type fermions (in particular, $b$-quark pairs) is opposite
to that of the Standard Model (SM), while at the same time all other tree-level
couplings are close to the SM values. We show that, whereas such a scenario is
consistent with current LHC observations, both future running at the LHC and a
future $e^+ e^-$ linear collider could determine the sign of the Higgs coupling
to $b$-quark pairs. Discrimination is possible for two reasons. First, the
interference between the $b$-quark and the $t$-quark loop contributions to the
$ggh$ coupling changes sign. Second, the charged-Higgs loop contribution to the
$\gamma \gamma h$ coupling is large and fairly constant up to the largest
charged-Higgs mass allowed by tree-level unitarity bounds when the $b$-quark
Yukawa coupling has the opposite sign from that of the SM (the change in sign
of the interference terms between the $b$-quark loop and the $W$ and $t$ loops
having negligible impact).
