Hybrid satellite-terrestrial networks (HSTNs) are considered to be a promising solution in dealing with coverage and mobility challenges encountered in 5 th generation (5G) networks that employ novel multiple access and connectivity schemes. In this respect, non-orthogonal multiple access (NOMA) as well as network coding (NC) schemes have attracted significant attention due to their performance gains which not only improve the quality of wireless transmission but also, effectively exploit the available spectrum. In this paper, a combined NOMA-NC (NNC) scheme is presented and integrated into an HSTN consisting of a low earth orbit (LEO) satellite belonging to an LEO constellation, a terrestrial base station (BS), and multiple terrestrial mobile terminals (MTs). The proposed scheme, termed HST-NNC, allows pairs of users to be simultaneously served through NOMA via the terrestrial BS link and the satellite link. Furthermore, the satellite employs random linear network coding (RLNC), within the general framework of systematic network coding (SNC), to improve the reception of the MTs when errors occur. The proposed HST-NNC, as compared to standalone NOMA, does not require additional channel state information (CSI) overheads because the satellite needs only the indices of user pairs to perform RLNC. Performance comparisons of HST-NNC with conventional orthogonal multiple access (OMA) and NOMA optimal user pairing schemes have shown that significant sum rate and BER gains can be obtained under various operating system parameters, such as varying number of MTs, and different channel conditions.