Essential for building quantum networks over remote independent nodes, the indistinguishability of photons has been extensively studied by observing the coincidence dip in the Hong-Ou-Mandel interferometer. However, indistinguishability is not limited to the same type of bosons. For the first time, we hereby observe quantum interference between flying photons and a single quantum of stored atomic coherence (magnon) in an atom-light beam splitter interface. We demonstrate that the Hermiticity of this interface determines the type of quantum interference between photons and magnons. Consequently, not only the bunching behavior that characterizes bosons is observed, but counterintuitively, fermionlike antibunching as well. The hybrid nature of the demonstrated magnon-photon quantum interface can be applied to versatile quantum memory platforms, and can lead to fundamentally different photon distributions from those occurring in boson sampling.