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We have fitted the k · p model derived recently by one of the authors [Klipstein, Phys. Rev. B 81, 235314 (2010)] to experimentally measured photoabsorption spectra at 77 and 300 K for representative InAs/GaSb superlattices with band-gap wavelengths between 4.3 and 10.5 μm. The model is able to reproduce the main features of the absorption spectra, including a strong peak from the zone boundary HH 2 → E 1 transition. We have also used the same model to predict the band-gap wavelengths of over 30 more superlattices, measured by photoluminescence spectroscopy. The maximum error is 0.6 μm, which corresponds to an uncertainty of less than 0.4 ML in layer width. This is comparable with the experimental uncertainty in layer widths, determined by in situ beam-flux measurements in the growth reactor. By eliminating all terms from the Hamiltonian, the energy contribution of which is less than the error due to the uncertainty in layer widths, the number of unknown fitting parameters has been reduced to six: two Luttinger parameters, three interface parameters, and the valence band offset. The remaining four Luttinger parameters are not independent and are determined from the two independent ones. Our set of Luttinger parameters is close to that reported by Lawaetz [Phys. Rev. B 4, 3460 (1971)], with a maximum deviation in any parameter of 0.6. The interface parameters are diagonal and have values of D S = 3 eVÅ, D X = 1.3 eVÅ, and D Z = 1.1 eVÅ at 77 K. The off-diagonal interface parameters α and β are too small to be fitted with any accuracy and have negligible effect on the unpolarized photoabsorption spectra. We also propose values for the room-temperature Luttinger and interface parameters. The fitted unstrained InAs/GaSb band overlap is 0.142 eV.