  If the Higgs boson decays to a pair of invisible particles, the number of
di-Higgs events, where each Higgs decay into Standard Model (SM) particles, are
reduced by a factor of two-third taking into account the current LHC bound on
invisible decay width of the Higgs boson. We investigate the sensitivity of the
upcoming high luminosity run of the LHC to di-Higgs production and subsequent
decay to dark matter in the context of the singlet scalar extension of the SM
augmented by a fermionic dark matter in the dark and bright channel
$\gamma\gamma+\not\!\! E_T$. Once systematic uncertainties on background yields
are considered, this dark and bright channel presents competitive limits than
$b\bar{b}+\not\!\! E_T$ after a careful tuning of the kinematical cuts that
raise the signal over background ratio. We further show that in a multivariate
analysis, for an invisible branching fraction as low as $\sim 10$%, we obtain
stronger bounds for the Higgs trilinear coupling from the
$\gamma\gamma+\not\!\! E_T$ channel compared to the $b\bar{b}\gamma\gamma$
final state. Finally, we demonstrate that the three channels
$\gamma\gamma+\not\!\! E_T$, $b\bar{b}+\not\!\! E_T$ and
$b\bar{b}\gamma\gamma$, complement each other in the search for di-Higgs
production with non-SM trilinear couplings when an invisible decay mode is
present.
