The process that contributes to the act of creating the structural organization of the midbrain-hindbrain boundary structure. The midbrain-hindbrain domain of the embryonic brain is comprised of the mesencephalic vesicle and the first rhombencephalic vesicle at early somitogenesis stages. An organizing center at the boundary patterns the midbrain and hindbrain primordia of the neural plate. [ GOC:jid GOC:dgh GOC:dph http://purl.obolibrary.org/obo/go/references/0000021 GOC:cls http://www.ncbi.nlm.nih.gov/pubmed/15541513 ]