  Higgs portal dark matter (DM) models are simple interesting and viable DM
models. There are three types of the models depending on the DM spin: scalar,
fermion and vector DM models. In this paper, we consider renormalizable,
unitary and gauge invariant Higgs portal DM models, and study how large
parameter regions can be surveyed at the International Linear Collider (ILC)
experiment at $\sqrt{s}=500$ GeV. For the Higgs portal singlet fermion and
vector DM cases, the force mediator involves two scalar propagators, the
SM-like Higgs boson and the dark Higgs boson. We show that their interference
generates interesting and important patterns in the mono-$Z$ plus missing $E_T$
signatures at the ILC, and the results are completely different from those
obtained from the Higgs portal DM models within the effective field theories.
In addition, we show that it would be possible to distinguish the spin of DM in
the Higgs portal scenarios, if the shape of the recoil-mass distribution is
observed. We emphasize that the interplay between these collider observations
and those in the direct detection experiments has to be performed in the model
with renomalizability and unitarity to combine the model analyses in different
scales.
