  The models that seek to explain the reflection spectrum in black hole
binaries usually invoke a point-like primary source of hard X-rays. This source
illuminates the accretion disk and gives rise to the discrete (lines) and
continuum-reflected components. The main goal of this work is to investigate
whether the extended, mildly relativistic jet that is present in black hole
binaries in the hard and hard-intermediate states is the hard X-ray source that
illuminates the accretion disk. We use a Monte Carlo code that simulates the
process of inverse Compton scattering in a mildly relativistic jet. Blackbody
photons from the thin accretion disk are injected at the base of the jet and
interact with the energetic electrons that move outward. Despite the fact that
the jet moves away from the disk at a mildly relativistic speed, we find that
approximately $15-20$\% of the input soft photons are scattered back toward the
accretion disk. The vast majority of the Comptonized, back-scattered photons
escape very close to the black hole ($h\lesssim 6 r_g$, where $r_g$ is the
gravitational radius), but a non-negligible amount escape at a wide range of
heights. At high heights, $h\sim 500-2000\,r_g$, the distribution falls off
rapidly. The high-height cutoff strongly depends on the width of the jet at its
base and is almost insensitive to the optical depth. The disk illumination
spectrum is softer than the direct jet spectrum of the radiation that escapes
in directions that do not encounter the disk. We conclude that an extended jet
is an excellent candidate source of hard photons in reflection models.
