The construction and operation of multi-layer heterogeneous satellite network (MLSNs) have gain significant attention due to its multiple capabilities and functionalities. This paper investigates the capacity performance of a two-layer geostationary earth orbit (GEO)/ low earth orbit (LEO) satellite network, where the non-orthogonal multiple access (NOMA) scheme is incorporated in a frequency coexistence scenario to improve the spectral efficiency. Specifically, a two-layer GEO/LEO satellite network framework is established by considering the dynamic properties and transmission characteristics of different satellites under practical environment. Then, the theoretical expression of achievable ergodic capacity is derived in terms of Meijer-G functions to evaluate the system performance effectively. Finally, simulation results are provided to validate the theoretical results, show the superiority of the employed NOMA scheme and analysis the impact of various system parameters on capacity performance of the considered network.