  In Neutrinophilic Two Higgs Doublet Models, Dirac neutrino masses are
obtained by forbidding a Majorana mass term for the right-handed neutrinos via
a symmetry. We study a variation of such models in which that symmetry is taken
to be a local U(1), leading naturally to the typical Lagrangian of the inverse
seesaw scenario. The presence of a new gauge boson and of an extended scalar
sector result in a rich phenomenology, including modifications to Z, Higgs and
kaon decays as well as to electroweak precision parameters, and a pseudoscalar
associated to the breaking of lepton number.
