  We perform a phenomenological study of the scalar sector of two models that
generate neutrino mass at the three-loop level and contain viable dark matter
candidates. Both models contain a charged singlet scalar and a larger scalar
multiplet (triplet or quintuplet). We investigate the effect of the extra
scalars on the Higgs mass and analyze the modifications to the triple Higgs
coupling. The new scalars can give observable changes to the Higgs decay
channel $h\rightarrow\gamma \gamma$ and, furthermore, we find that the
electroweak phase transition becomes strongly first-order in large regions of
parameter space.
