  A fermion dark matter candidate with a relic abundance set by annihilation
through a pseudoscalar can evade constraints from direct detection experiments.
We present simplified models that realize this fact by coupling a fermion dark
sector to a two-Higgs doublet model. These models are generalizations of mixed
bino-Higgsino dark matter in the MSSM, with more freedom in the couplings and
scalar spectra. Annihilation near a pseudoscalar resonance allows a significant
amount of parameter space for thermal relic dark matter compared to
singlet-doublet dark matter, in which the fermions couple only to the SM Higgs
doublet. In a general two-Higgs doublet model, there is also freedom for the
pseudoscalar to be relatively light and it is possible to obtain thermal relic
dark matter candidates even below 100 GeV. In particular, we find ample room to
obtain dark matter with mass around 50 GeV and fitting the Galactic Center
excess in gamma-rays. This region of parameter space can be probed by LHC
searches for heavy pseudoscalars or electroweakinos, and possibly by other new
collider signals.
