We report experimentally observed magnetic domain-wall structures in antiferromagnetically coupled multilayer films with perpendicular anisotropy. Our studies reveal a first-order phase transition from domain walls with no net moment to domain walls with ferromagnetic cores. The transition originates from the competition between dipolar and exchange energies, which we tune by means of layer thickness. Although observed in a synthetic antiferromagnetic system, such domain-wall structures may be expected to occur in A-type antiferromagnets with anisotropic exchange coupling.