Aluminum nitride (AlN) film coatings on flexible substrates (polymeric Teflon, Mylar) have been obtained using a hybrid helicon-arc ion-plasma deposition technique with high adhesion of coatings. Studies of optical, morphological, and structural properties of AlN films have been carried out. It was found that AlN coatings on Teflon and Mylar thin-film substrates substantially suppress transmission of infrared (IR) radiation within the spectral range λ ∼ 5–20 μm at certain technological parameters and thickness of AlN. Transmission in THz regions by using quasioptics attains T ≈ 79%–95%, and losses measured in the channels within the microwave region 2 to 36 GHz are <0.06 dB. The obtained composite structures (AlN coatings on Teflon and Mylar thin-film substrates), due to a high thermal conductivity of AlN, could be used as efficient blocking structures in the infrared spectral range (“infrared stealth”) withdrawing the heat from filters warmed by IR radiation. At the same time, they can be used as the transparent ones in the microwave and THz regions, which can be important for low-temperature detector components of navigation, positioning, and telecommunication systems due to reducing the background noise.