  In this paper, we explore a scenario where the dark matter is a mixture of
interacting and non interacting species. Assuming dark matter-photon
interactions for the interacting species, we find that the suppression of the
matter power spectrum in this scenario can mimic that expected in the case of
massive neutrinos. Our numerical studies include present limits from Planck
Cosmic Microwave Background data, which render the strength of the dark matter
photon interaction unconstrained when the fraction of interacting dark matter
is small. Despite the large entangling between mixed dark matter and neutrino
masses, we show that future measurements from the Dark Energy Instrument (DESI)
could help in establishing the dark matter and the neutrino properties
simultaneously, provided that the interaction rate is very close to its current
limits and the fraction of interacting dark matter is at least of
$\mathcal{O}\left(10\%\right)$. However, for that region of parameter space
where a small fraction of interacting DM coincides with a comparatively large
interaction rate, our analysis highlights a considerable degeneracy between the
mixed dark matter parameters and the neutrino mass scale.
