Interband absorption of light in bismuth nanostructures has been studied in the framework of a complex model for electron spectrum of Bi, such as the Cohen model, the Abrikosov-Falkovsky model, and the McClure model. The obtained results differ qualitatively from those obtained in the framework of simple band models, such as the parabolic band model and the Lax two-band model. It is shown that both the interband transition with quantum number conservation and the interband transition without quantum number conservation are allowed in the framework of complex models for electron energy spectrum of Bi. Due to the interband transitions without quantum number conservation (these transitions are forbidden in simple band models), the peak of optical absorption in measured spectra can occur at lower photon energies than in the spectra simulated in the framework of simple band models. A similar difference between the peaks was observed by Black et al. in Bi nanowires. The interband transitions without quantum number conservation substantially complicate the oscillation pattern and the identification of absorption peaks. The frequency dependence of the coefficient of interband absorption calculated in the framework of the McClure model has pronounced peaks, whereas in the simple band models this dependence has a step-like pattern. It is concluded that the McClure model enables the oscillation behavior of interband absorption in bismuth nanostructures to be properly described.