Reconfigurable intelligence surface (RIS) and unmanned aerial vehicle (UAV) has been recently applied in mobile edge computing (MEC) networks to enhance communication capacity. However, scatterers often obstruct the channel between UAV and user equipment (UE), causing poor quality of service in urban scenarios. To tackle this problem, this paper proposes and evaluates UAV-mounted RIS (U-RIS) assisted UAV communications incorporating non-orthogonal multiple access (NOMA) networks. The UE's transmit power, the RIS's phase shift, and the UAV and U-RIS's trajectories are jointly optimized for maximizing the communication capacity of the considered networks. The block coordinate descent (BCD)-based iterative algorithm is developed to solve the joint non-convex optimization problem. The grid search (GS) method is used for trajectory optimation. Numerical results show that the NOMA scheme has significantly improved the communication capacity, but RIS has limited gain.