Magnetization, nuclear magnetic resonance, high-resolution x-ray diffraction and magnetic field-dependent neutron diffraction measurements reveal a novel magnetic ground state of Ba{0.60}K{0.40}Mn2As2 in which itinerant ferromagnetism (FM) below a Curie temperature TC = 100 K arising from the doped conduction holes coexists with collinear antiferromagnetism (AFM) of the Mn local moments that order below a Neel temperature TN = 480 K. The FM ordered moments are aligned in the tetragonal ab-plane and are orthogonal to the AFM-ordered Mn moments that are aligned along the c-axis. The magnitude and nature of the low-T FM ordered moment correspond to complete polarization of the doped-hole spins (half-metallic itinerant FM) as deduced from magnetization and ab-plane electrical resistivity measurements.