LaBaCuFeO 5 + δ (LaBCFO) exhibits an irreversible magnetic behavior below T=68(3) K. The local structure around the Cu and Fe atoms studied by EXAFS reveals distortions in the internal shells of the coordination polyhedra of these atoms. A magnetic model could be satisfactorily refined from neutron powder diffraction data, with a magnetic unit cell with lattice parameters related to the structural constants as a M =3a/2, b M =b/2 and c M =c/2. This model introduces the existence of randomly distributed magnetic centers in the structure, in agreement with the irreversibility observed by the DC susceptibility measurements. The oxygen disorder including vacancies and the shift in the position of the non-stoichiometric oxygen atoms produced by the imperfect La/Ba replacement in the packing are considered to be key for the magnetic behavior of the LaBCFO.