This paper leverages stochastic geometry to model, analyze, and optimize multi-band unmanned aerial vehicle (UAV) communication networks operating across low-frequency and millimeter-wave (mmWave) bands. We introduce a novel approach to modeling mmWave antenna gain in such networks, which allows us to better capture and account for interference in our analysis and optimization. We then propose a simple yet effective user-UAV association policy, which strategically biases users towards mmWave UAVs to take advantage of lower interference and wider bandwidths compared to low-frequency UAVs. Under this scheme, we analytically derive the corresponding association probability, coverage probability, and spectral efficiency. We conclude by assessing our proposed association policy through simulation and analysis, demonstrating its effectiveness based on coverage probability and per-user data rates, as well as the alignment between analytical and simulation results.