Mueller matrix ellipsometry over the wide spectral range from the mid-IR to UV is applied to characterize the dielectric function tensor for films of densely packed single-walled carbon nanotubes aligned in the surface plane. These films optically act as metamaterials with an in-plane anisotropic, bulk effective medium response. A parameterized oscillator model is developed to describe electronic interband transitions, π - π ∗ plasmon resonances, and free-carrier absorption. Wide ranges of hyperbolic dispersion are observed and exceptional tuneability of the hyperbolic ranges is demonstrated by comparing results for a film of aligned but unordered carbon nanotubes with a film fabricated under optimized conditions to achieve hexagonally close-packed alignment of the nanotubes. The effect of doping on the optical properties and hyperbolic range is discussed.