Quantum magnets display a wide variety of collective excitations, including spin waves (magnons), coherent singlet-triplet excitations (triplons), and pairs of fractional spins (spinons). These modes differ radically in nature and properties, and in all conventional analyses any given material is interpreted in terms of only one type. We report inelastic neutron scattering measurements on the spin-1/2 antiferromagnet SeCuO3, which demonstrate that this compound exhibits all three primary types of spin excitation. Cu-2 sites form strongly bound dimers while Cu-2 sites form a network of spin chains, whose weak three-dimensional (3D) coupling induces antiferromagnetic order. We perform quantitative modeling to extract all of the relevant magnetic interactions and show that magnons of the Cu-2 system give a lower bound to the spinon continua, while the Cu-2 system hosts a band of high-energy triplons at the same time as frustrating the 3D network.