  We investigate an extension of the $\Lambda$CDM model where the dark matter
(DM) is coupled to photons, inducing a nonconservation of the numbers of
particles for both species, where the DM particles are allowed to dilute
throughout the cosmic history with a small deviation from the standard
evolution decaying into photons, while the associated scattering processes are
assumed to be negligible. In addition, we consider the presence of massive
neutrinos with the effective number of species $N_{\rm eff}$ as a free
parameter. The effects of the DM-photon coupling on the cosmic microwave
background (CMB) and matter power spectra are analyzed. We derive the
observational constraints on the model parameters by using the data from CMB,
baryonic acoustic oscillation (BAO) measurements, the recently measured new
local value of the Hubble constant from the Hubble Space Telescope, and large
scale structure (LSS) information from the abundance of galaxy clusters. The
DM-photon coupling parameter $\Gamma_{\gamma }$ is constrained to
$\Gamma_{\gamma } \leq 1.3 \times10^{-5}$ (at 95\% C.L.) from the joint
analysis carried out by using all the mentioned data sets. The neutrino mass
scale $\sum m_{\nu}$ upper bounds at 95\% C.L. are obtained as $\sum m_{\nu}
\sim 0.9$ eV and $\sum m_{\nu} \sim 0.4$ eV with and without the LSS data,
respectively. We observe that the DM-photon coupling cause significant changes
in the best fit value of $N_{\rm eff}$ but yields statistical ranges of $N_{\rm
eff}$ compatible with the standard predictions, and we do not find any evidence
of dark radiation. Due to nonconservation of photons in our model, we also
evaluate and analyze the effects on the BAO acoustic scale at the drag epoch.
The DM-photon coupling model yields high values of Hubble constant consistent
with the local measurement, and thus alleviates the tension on this parameter.
