The general study of the ontology of quantum field theories (QFTs) concerns whether particles or fields are more fundamental. Both views are well-motivated, although each is subject to some serious criticism. Given that the current versions of the particle interpretation and the field interpretation are not satisfying, I propose a mixed ontology of particles and fields in the framework of QFT. I argue that the ontological question should focus on how to view particles and fields consistently in QFT, provided that (...) they are the natural candidates for the ontology of QFT. In particular, based on this reading, I adopt a functionalist reading of ontology and defend a mixed ontology of QFT. I address a paradigmatic case of the mixed ontology approach: a particle/field duality defined in terms of functional equivalence between particles and fields. Functionalism about ontology provides new insight into resolving the problem of unitarily inequivalent representations, which is one of the major interpretational issues of QFT. (shrink)