A spectrum-sharing satellite-ground integrated network is conceived, consisting of a pair of non-geostationary orbit (NGSO) constellations and multiple terrestrial base stations, which impose the co-frequency interference (CFI) on each other. The CFI may increase upon increasing the number of satellites. To manage the potentially severe interference, we propose to rely on joint multi-domain resource aided interference management (JMDR-IM). Specifically, the coverage overlap of the constellations considered is analyzed. Then, multi-domain resources - including both the beam-domain and power-domain - are jointly utilized for managing the CFI in an overlapping coverage region. This joint resource utilization is performed by relying on our specifically designed beam-shut-off and switching based beam scheduling, as well as on long short-term memory based joint autoregressive moving average assisted deep Q network aided power scheduling. Moreover, the outage probability (OP) of the proposed JMDR-IM scheme is derived, and the asymptotic analysis of the OP is also provided. Our performance evaluations demonstrate the superiority of the proposed JMDR-IM scheme in terms of its increased throughput and reduced OP.