  We present a complete halo model for mixed dark matter composed of cold dark
matter (CDM) and ultralight axion-like particles (ULAs). Our model treats ULAs
as a biased tracer of CDM, in analogy to treatments of massive neutrinos and
neutral hydrogen. The model accounts for clustering of ULAs around CDM host
halos, and fully models the cross correlations of both components. The model
inputs include the ULA Jeans scale, and soliton density profile. Our model can
be used to predict the matter power spectrum, $P(k)$, on non-linear scales for
sub-populations of ULAs across the mass range $10^{-33}\text{ eV}\leq m\leq
10^{-21}\text{ eV}$, and can be calibrated against future mixed DM simulations
to improve its accuracy. The mixed DM halo model also allows us to assess the
importance of various approximations.
