This paper investigates the achievable rate maximization problem of a downlink unmanned aerial vehicle (UAV)-enabled communication system aided by an intelligent omni-surface (IOS). Different from the state-of-the-art reconfigurable intelligent surface (RIS) that only reflects incident signals, the IOS can simultaneously reflect and transmit the signals, thereby providing full-dimensional rate enhancement. To tackle such a problem, we formulate it by jointly optimizing the IOS's phase shift and the UAV trajectory. Although it is difficult to solve it optimally due to its non-convexity, we propose an efficient iterative algorithm to obtain a high-quality suboptimal solution. Simulation results show that the IOS-assisted UAV communications can achieve more significant improvement in achievable rates than other benchmark schemes.