We jointly consider full-duplex operation and network coding in two-hop relay networks to enhance the throughput of the block transmission of packets over erasure channels. Two coded transmission schemes, termed Fewest Broadcast Packet First (FBPF) and Buffer Contents-based Coded Transmission (BCCT), are proposed, where random linear network coding is employed at the Base Station (BS) and the Relay Station (RS), respectively. Both schemes do not rely on users’ Channel State Information (CSI), buffer status, channel parameters, etc., and hence are practically viable. We derive closed-form upper bounds on the throughput of both schemes. We prove that both schemes achieve the optimal throughput when the BS-to-RS channel is perfect. Through extensive simulations, we demonstrate that both schemes incur substantially higher throughput than the traditional uncoded Automatic Repeat-reQuest (ARQ) scheme and perform close to a general upper bound on the system throughput. Furthermore, even with imperfect Self-Interference Cancellation (SIC) at the full-duplex RS, our schemes are shown to be superior to state-of-the-art coded transmission schemes designed for half-duplex relay networks, given that the impact of imperfect SIC on the BS-to-RS channel quality is not high.