139La- and 55Mn-NMR spectra demonstrate that the ground state of the A-site-ordered perovskite manganite LaBaMn2O6 is a spatial mixture of the ferromagnetic and antiferromagnetic regions, which are assigned to the metallic and the insulating charge ordered state, respectively. This exotic coexisting state appears below 200 K via a first-order-like formation of the antiferromagnetic charge ordered state inside the ferromagnetic metal one. The Mn spin-spin relaxation rate indicates that the ferromagnetic region coexisting with the antiferromagnetic one in LaBaMn2O6 is identical to the bulk ferromagnetic metal phase of the disordered form La0.5Ba0.5MnO3 in spite of the absence of A-site disorder. This suggests a mesoscopic rather than nanoscopic nature of the ferromagnetic region in LaBaMn2O6.