In recent years, ultracold atoms have emerged as a unique tool to engineer and study novel experimental systems, furthering our understanding of quantum many-body physics. For bosons, their advent has permitted the study of weakly interacting Bose-Einstein condensates, two-dimensional gases or the superfluid-Mott insulator transition. For fermions with attractive interaction the observation of BEC-BCS crossover demonstrated the connexion between Bose-Einstein condensation (BEC) and fermionic superfluidity described by Bardeen, Cooper and Schrieffer's theory (BCS). Here, we report on the first production of a mixture of bosons and fermions where both species are superfluid. Such a mixture has been long sought in liquid helium where superfluidity has been achieved separately in both bosonic 4He and fermionic 3He. However, due to strong interactions between the two isotopes, 3He-4He mixtures contain a small fraction of 3He (typically 6%) which, so far, has prevented reaching simultaneous superfluidity for the two species. With cold atoms, a Fermi sea mixed with a BEC has been observed. In this work we tune a cloud of lithium isotopes to a regime where the mixture of bosonic and fermionic superfluids is stable. We probe the collective dynamics of this system by exciting center-of-mass oscillations that exhibit extremely low damping. Using high precision spectroscopy of these low-lying modes we observe coherent energy exchange and measure the coupling between the two superfluids. We interpret our observations by a simple coupled oscillator model