We present infrared spectra (0.1–1 eV) of electrostatically gated bilayer graphene as a function of doping and compare it with tight-binding calculations. All major spectral features corresponding to the expected interband transitions are identified in the spectra: a strong peak due to transitions between parallel split-off bands and two onset-like features due to transitions between valence and conduction bands. A strong gate voltage dependence of these structures and a significant electron-hole asymmetry are observed that we use to extract several band parameters. The structures related to the gate-induced band gap are less pronounced in the experiment than predicted by the tight-binding model that uses parameters obtained from previous experiments on graphite and recent self-consistent band-gap calculations.