The physical properties of epitaxial films can fundamentally differ from those of bulk single crystals even above the critical thickness. By a combination of non-resonant x-ray magnetic scattering, neutron diffraction and vector-mapped x-ray magnetic linear dichroism photoemission electron microscopy, we show that epitaxial (111)-BiFeO3 films support sub-micron antiferromagnetic domains, which are magneto-elastically coupled to a coherent crystallographic monoclinic twin structure. This unique texture, which is absent in bulk single crystals, should enable control of magnetism in BiFeO3 film devices via epitaxial strain.