We demonstrate that in a weak-coupled two-band superconducting slab the interaction between vortices penetrating the sample and its boundaries leads to the phenomenon of vortex splitting, which divides composite vortices and creates fractional ones. The interaction between vortices, attractive for different bands and repulsive for the same band, which is controlled by the electric current density flowing through the system, leads to an ordered alternating arrangement of the vortices. This arrangement creates nonequilibrium interband phase textures or domains with different signs of the Josephson energy of the interaction between the band condensates. Such phase textures have a significant effect on the dissipation caused by the vortex motion. In particular, in the phase-texture regime the onset of the dissipation is shifted to higher current densities.