We create atom-molecule superpositions in a Bose-Fermi mixture of Rb-87 and K-40 atoms. The superpositions are generated by ramping an applied magnetic field near an interspecies Fano-Feshbach resonance to coherently couple atom and molecule states. Rabi- and Ramsey-type experiments show oscillations in the molecule population that persist as long as 150 microseconds and have up to 50% contrast. The frequencies of these oscillations are magnetic-field dependent and consistent with the predicted molecule binding energy. This quantum superposition involves a molecule and a pair of free particles with different statistics (i.e. bosons and fermions), and furthers exploration of atom-molecule coherence in systems without a Bose-Einstein condensate.