In this paper, we consider a two-hop molecular communication network consisting of one nanotransmitter, one nanoreceiver, and one nanotransceiver acting as a relay. We consider two different schemes for relaying to improve the range of diffusion-based molecular communication. In the first scheme, two different types of messenger molecules are utilized at the relay node for transmission and detection. In the second scheme, we assume that there is only one type of molecule available to be used as an information carrier. We identify self-interference as the performance-limiting effect for the second relaying scheme. Self-interference occurs when the relay must detect the same type of molecule that it also emits. Furthermore, we consider two relaying modes analogous to those used in wireless communication systems, i.e., full-duplex and half-duplex. In particular, while our main focus is on full-duplex relaying, half-duplex relaying is employed as a means to mitigate self-interference. In addition, we propose the adaptation of the decision threshold as an effective mechanism to mitigate self-interference at the relay for full-duplex transmission. We derive closed-form expressions for the expected error probability of the network for both considered relaying schemes.