Magnetization, nuclear magnetic resonance, high-resolution x-ray diffraction, and magnetic field-dependent neutron diffraction measurements reveal a novel magnetic ground state of Ba0.60K0.40Mn2As2 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 Néel 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.