In this paper, we consider full-duplex (FD) relay networks with filter-and-forward (FF)-based multiple relays (FD-FF), where relay filters jointly mitigate self-interference (SI), inter-relay interference (IRI), and inter-symbol interference. We consider the filter design problem based on signal-to-noise-plus-interference ratio maximization subject to a total relay transmit power constraint. To make the problem tractable, we propose two methods: one that imposes an additional constraint whereby the filter responses to SI and IRI are nulled, and the other that makes i.i.d. assumptions on the relay transmit signals. Simulation results show that the proposed FD-FF scheme outperforms a conventional FF scheme in half-duplex mode. We also consider the filter design when only second-order statistics of channel path gains are available.