  Some optomechanical systems can be transparent to a probe field when a strong
driving field is applied. These systems can provide an optomechanical analogue
of electromagnetically-induced transparency (EIT). We study the transmission of
a probe field through a hybrid optomechanical system consisting of a cavity and
a mechanical resonator with a two-level system (qubit). The qubit might be an
intrinsic defect inside the mechanical resonator, a superconducting artificial
atom, or another two-level system. The mechanical resonator is coupled to the
cavity field via radiation pressure and to the qubit via the Jaynes-Cummings
interaction. We find that the dressed two-level system and mechanical phonon
can form two sets of three-level systems. Thus, there are two transparency
windows in the discussed system. We interpret this effect as an optomechanical
analog of two-color EIT (or double-EIT). We demonstrate how to switch between
one and two EIT windows by changing the transition frequency of the qubit. We
show that the absorption and dispersion of the system are mainly affected by
the qubit-phonon coupling strength and the transition frequency of the qubit.
