  We solve the problem of the transmission and reflection of phonons and rotons
at the interface between superfluid helium and a solid, for all angles of
incidence and in both directions. A consistent solution of the problem is
presented which allows us to rigorously describe the simultaneous creation of
phonons, $R^-$, and $R^+$ rotons in helium by either a phonon from the solid or
a helium quasiparticle incident on the interface. The interaction of all $HeII$
quasiparticles with the interface, and their transmission, reflection and
conversion into each other, is described in a unified way. The angles of
propagation and the probabilities of creating quasiparticles are obtained for
all cases. Andreev reflection of helium phonons and rotons is predicted. The
energy flows through the interface due to phonons, $R^-$, and $R^+$ rotons are
derived. The small contribution of the $R^-$ rotons is due to the small
probability of an $R^-$ roton being created by a phonon in the solid, and vice
versa. This explains the failure to directly create beams of $R^-$ rotons prior
to the experiments of Tucker and Wyatt in 1999. New experiments for creating
$R^-$ rotons, by beams of high-energy phonons (h-phonons), are suggested.
