Terahertz (THz) band unmanned aerial vehicle (UAV) links exploit ultra-wide spectra and high directivity to deliver multi-Gbps secure data for remote sensing and wireless backhaul, but their open three-dimensional flight paths increase vulnerability to covert detection and jamming. Altitude-dependent atmospheric loss, negligible in microwave or terrestrial THz studies, becomes critical in this band owing to triple selectivity, where propagation varies sharply with frequency, distance, and environment. In this paper, a spatially-aware transmission framework is proposed that jointly allocates spectrum and power according to node altitude and beam orientation to maximize jam-resilience covert throughput. Specifically, a three-dimensional propagation model incorporating altitude-dependent molecular absorption, weather loss, and turbulence is established, closed-form expressions for covert outage probability and throughput are derived, and the resulting nonconvex band-wise optimization is solved. Simulation results verify significant gains in covert throughput and jamming robustness and reveal that downward transmissions are more secure than upward counterparts, as their propagation path traverses denser and more absorptive air, whereas the upward path quickly rises into thinner layers that expose the signal to remote eavesdroppers. These analytical insights furnish a quantitative basis for altitude-aware spectrum planning and multilayer topology design in future space-air-ground integrated networks.