In the present work, we consider the dynamics of dark solitons as one mode of
a defocusing photorefractive lattice coupled with bright solitons as a second
mode of the lattice. Our investigation is motivated by an experiment which
illustrates that such coupled states can exist with both components in the
first gap of the linear band spectrum. This finding is further extended by the
examination of different possibilities from a theoretical perspective, such as
symbiotic ones where the bright component is supported by states of the dark
component in the first or second gap, or non-symbiotic ones where the bright
soliton is also a first-gap state coupled to a first or second gap state of the
dark component. While the obtained states are generally unstable, these
instabilities typically bear fairly small growth rates which enable their
observation for experimentally relevant propagation distances.