Perovskite superlattices have received enormous attention in recent years, for they possess several new phases of quantum matter. In particular, an unexpected exchange bias effect in (111)-oriented superlattices composed of ferromagnetic LaMnO₃ and paramagnetic LaNiO₃ is observed, which has aroused broad interest. In this work, three kinds of LaMnO₃/LaNiO₃ superlattices with (001), (110), and (111) out-of-plane orientation are fabricated by pulsed laser deposition, and also studied systemically. It is found that the superlattices are epitaxially grown on the SrTiO₃ substrates without strain relaxation. The superlattices have a monolayer terraced structure with a surface roughness below 0.1 nm. Electrical transport measurements reveal a Mott conducting behavior with strong localization of electrons in the superlattices. All the superlattices with different orientations exhibit exchange bias phenomenon. The field cooling and zero field cooling curves indicate that there are two different magnetic components in the superlattice in a low temperature range. Further analysis of the values of exchange field reveals that the exchange bias field is related to the orientation and polarity of the superlattices. Different superlattices form different charged planes stacked along out-of-plane orientation, leading to a polarity match/mismatch at the interface between the superlattices and substrates. The surface reconstructions that act as compensating for the polar mismatch influence the exchange bias field of the superlattices. It is observed that the intensities of the exchange field of the polar-matched superlattices are higher than those of the polar-mismatched superlattices at different temperatures. These results are helpful in further understanding the magnetoelectric transport properties in the perovskite superlattices.