  If dark matter (DM) consists of primordial black holes (PBHs) and particles
simultaneously, PBHs are generically embedded within particle DM halos. Such
"dressed PBHs" (dPBHs) are not subject to typical PBH constraints and can
explain the DM abundance in the mass range $10^{-1} \sim 10^2 M_\odot$. We show
that diffractive lensing of chirping gravitational waves (GWs) from binary
mergers can not only discover, but can also identify dPBH lenses and
discriminate them from bare PBHs on the event-by-event basis, with potential to
uniquely establish the co-existence of subdominant PBHs and particle DM.
