We look for domain wall and textured vortex solutions in a two-component Ginzburg-Landau model inspired by two-band superconductivity. The two-dimensional two-component model, with equal coherence lengths and no magnetic field, shows some interesting properties. In the absence of a Josephson type coupling between the two order parameters a ''textured vortex'' is found by analytical and numerical solution of the Ginzburg-Landau equations. With a Josephson type coupling between the two order parameters we find the system to split up in two domains separated by a domain wall, where the order parameter is depressed to zero.