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We explore simple Higgs-portal models of dark matter (DM) with spin 1/2, 3/2,and 1, respectively, applying to them constraints from the LUX and PandaX-IIdirect detection experiments and from LHC measurements on the 125-GeV Higgsboson. With only one Higgs doublet, we find that the spin-1/2 DM having apurely scalar effective coupling to the doublet is viable only in a narrowrange of mass near the Higgs pole, whereas the vector DM is still allowed ifits mass is also close to the Higgs pole or exceeds 1.4 TeV, both in line withearlier analyses. Moreover, the spin-3/2 DM is in a roughly similar situationto the spin-1/2 DM, but has surviving parameter space which is even morerestricted. We also consider the two-Higgs-doublet extension of each of thepreceding models, assuming that the expanded Yukawa sector is that of thetwo-Higgs-doublet model of type II. We show that in thesetwo-Higgs-doublet-portal models significant portions of the DM mass regionsexcluded in the simplest scenarios by direct search bounds can be reclaimed dueto suppression of the effective DM interactions with nucleons at some ratios ofthe $CP$-even Higgs bosons' couplings to the up and down quarks. The regainedparameter space contains areas which can yield a DM-nucleon scatteringcross-section that is far less than its current experimental limit or even goesbelow the neutrino-background floor.

Two-Higgs-Doublet-Portal Dark-Matter Models in Light of Direct Search and LHC Data