  We investigate an electroweak interacting dark matter (DM) model in which the
DM is the neutral component of the SU$(2)_L$ triplet fermion that couples to
the standard model (SM) Higgs sector via an SM singlet Higgs boson. In this
setup, the DM can have a CP-violating coupling to the singlet Higgs boson at
the renormalizable level. As long as the nonzero Higgs portal coupling
(singlet-doublet Higgs boson mixing) exists, we can probe CP violation of the
DM via the electric dipole moment of the electron. Assuming the
$\mathcal{O}(1)$ CP-violating phase in magnitude, we investigate the
relationship between the electron EDM and the singlet-like Higgs boson mass and
coupling. It is found that for moderate values of the Higgs portal couplings,
current experimental EDM bound is not able to exclude the wide parameter space
due to a cancellation mechanism at work. We also study the spin-independent
cross section of the DM in this model. It is found that although a similar
cancellation mechanism may diminish the leading-order correction, as often
occurs in the ordinary Higgs portal DM scenarios, the residual higher-order
effects leave an $\mathcal{O}(10^{-47})~{\rm cm}^2$ correction in the
cancellation region. It is shown that our benchmark scenarios would be fully
tested by combining all future experiments of the electron EDM, DM direct
detection and Higgs physics.
