  We study the experimental constraints on a model of a two-component dark
matter, consisting of the QCD axion, and a scalar particle, both contributing
to the dark matter relic abundance of the Universe. The global Peccei-Quinn
symmetry of the theory can be spontaneously broken down to a residual
$\mathbb{Z}_2$ symmetry, thereby identifying this scalar as a stable weakly
interacting massive particle, i.e., a dark matter candidate, in addition to the
axion. We perform a comprehensive study of the model using the latest data from
dark matter direct and indirect detection experiments, as well as new physics
searches at the Large Hadron Collider. We find that although the model is
mostly constrained by the dark matter detection experiments, it is still viable
around a small region of the parameter space where the scalar dark matter is
half as heavy as the Standard Model Higgs. In this allowed region, the bounds
from these experiments are evaded due to a cancellation mechanism in the dark
matter--Higgs coupling. The collider search results, however, are shown to
impose weak bounds on the model.
