  The analytical phase-space distribution function (DF) of spherical
self--consistent galaxy (or cluster) models, embedded in a dark matter halo,
where both density distributions follow the Hernquist profile, with different
total masses and core radii (hereafter called HH models), is presented. The
concentration and the amount of the stellar and dark matter distributions are
described by four parameters: the mass and core radius of the {\it reference}
component, and two dimensionless parameters describing the mass and core radius
of the {\it halo} component. A variable amount of orbital anisotropy is allowed
in both components, following the widely used parameterization of
Osipkov-Merritt. An important case is obtained for a null core radius of the
halo, corresponding to the presence of a central black hole (BH). It is proved
that globally isotropic HH models are consistent for any mass ratio and core
radii ratio, even in the case of a central BH. In this last case the analytical
expression for a lower limit of the anisotropy radius of the host system as a
function of the BH mass is given. In the particular case of global isotropy the
stability of HH models is proved, and the stability of radially anisotropic HH
models is briefly discussed. The expression derived for the DF is useful for
understanding the relations between anisotropy, density shape and external
potential well in a consistent stellar system, and to produce initial
conditions for N-body simulations of two-component galaxies or galaxy clusters.
