  We introduce a linearized bi-metric theory of gravity with two metrics. The
metric g_{ab} describes null hypersurfaces of the gravitational field while
light moves on null hypersurfaces of the optical metric \bar{g}_{ab}.
Bi-metrism naturally arises in vector-tensor theories with matter being
non-minimally coupled to gravity via long-range vector field. We derive
explicit Lorentz-invariant solution for a light ray propagating in space-time
of the bi-metric theory and disentangle relativistic effects associated with
the two metrics. This anlysis can be valuable for future spaceborne laser
missions ASTROD and LATOR dedicated to map various relativistic gravity
parameters in the solar system to unparalleled degree of accuracy.
