  We study a fermionic dark matter model in which the interaction of the dark
and visible sectors is mediated by Higgs portal type couplings. Specifically,
we consider the mixing of a dark sector scalar with the scalars of a Two Higgs
Doublet Model extension of the Standard Model. Given that scalar exchange will
result in a spin-independent dark matter-nucleon scattering cross section, such
a model is potentially subject to stringent direct detection constraints.
Moreover, the addition of new charged scalars introduce non-trivial flavour
constraints. Nonetheless, this model allows more freedom than a standard Higgs
portal scenario involving a single Higgs doublet, and much of the interesting
parameter space is not well approximated by a Simplified Model with a single
scalar mediator. We perform a detailed parameter scan to determine the mass and
coupling parameters which satisfy direct detection, flavour, precision
electroweak, stability, and perturbativity constraints, while still producing
the correct relic density through thermal freezeout.
