In this paper, we present an analytical approach to evaluate the performance of dual-hop, two-way, and asymmetric device-to-device (D2D) communications with and without network coding. In our approach, we first establish a relationship between link outage probability (LOP) and packet loss probability (PLP), where PLP is defined as a function of LOP. By distinguishing between two types of probabilities, we then investigate the system throughput and end-to-end packet loss probability (E2EPLP). Our evaluation results reveal that when PLPs of all links along one-way D2D communications are greater or smaller than those of their corresponding links along the other direction, network coding can achieve higher throughput (about 25%), as well as an lower E2EPLP (approximately 10%). We believe that the proposed analytical approach can provide a useful insight into the application of network coding in relay-based D2D networks.