  Motivated by the neutrino data, an extension of the Standard Model with three
Higgs-boson doublets has been proposed. Imposing an O(2) x Z2 family symmetry,
a neutrino mixing matrix with theta23 = pi/4 and theta13 = 0 appears in a
natural way. Even though these values for the mixing matrix do not follow the
recent experimental constraints, they are nevertheless a good approximation. We
study the Higgs potential of this model in detail. We apply recent methods
which allow for the study of any three-Higgs-boson doublet model. It turns out
that for a variety of parameters the potential is stable, has the correct
electroweak symmetry breaking, and gives the correct vacuum expectation value.
