  In the lepton-specific version of two Higgs doublet models, a discrete
symmetry is used to couple one Higgs, $\Phi_2$, to quarks and the other,
$\Phi_1$, to leptons. The symmetry eliminates tree level flavor changing
neutral currents (FCNC). Motivated by strong constraints on such currents in
the quark sector from meson-antimeson mixing, and by hints of $h \to \mu\tau$
in the lepton sector, we study a simple three Higgs doublet model in which one
doublet couples to quarks and the other two to leptons. Unlike most other
studies of three Higgs doublet models, we impose no flavor symmetry and just
use a $Z_2$ symmetry to constrain the Yukawa couplings. We present the model
and discuss the various mixing angles. Constraining the parameters to be
consistent with observations of the Higgs boson at the LHC, we study the
properties of the charged Higgs boson(s) in the model, focusing on the case in
which the charged Higgs is above the top threshold. It is found that one can
have the branching fraction of the charged Higgs into $\tau\nu_\tau$ comparable
to $t\bar{b}$ decay without needing very large values for the ratios of vevs.
One can also get a large branching fraction for the much more easily observable
$\mu\nu_\tau$ decay.
