  In light of the Higgs boson discovery, we explore mono-Higgs signature in
association with dark matter pair production at the LHC in a renormalizable
model with a fermionic dark matter candidate. For two channels with
$\gamma\gamma+\text{MET}$ and $b \bar b+\text{MET}$ in the final state we
simulate the SM backgrounds and signal events at $\sqrt{s} = 14$ TeV. We then
estimate the LHC sensitivities for various benchmark points for two integrated
luminosities ${\cal L} = 300~\text{fb}^{-1}$ and ${\cal L} = 3~
\text{ab}^{-1}$. We constrain the Yukawa coupling of the dark matter-SM
interaction, taking into account bounds from mono-Higgs signature, observed
dark matter relic density, Higgs physics, perturbativity requirement and
electroweak measurements. Concerning the mono-Higgs search, it turns out that
the channel with the largest branching ratio, $b \bar b$ channel, provides
better sensitivity. There are found regions in the parameter space of the model
compatible with all the bounds mentioned above which can be reached in future
LHC studies.
