Spectroscopic ellipsometry is used to measure the dielectric function of heavily doped p-type GaAs for wave numbers from 100 to 2000 cm-1. Due to partial filling of the heavy- and light-hole valence bands, heavy holes as well as light holes form a multiple-component plasma coupled with longitudinal optical phonons. Line-shape analysis of the infrared response allows differentiating between light- and heavy-hole contributions to the carrier plasma, and the results observed suggest nonparabolicity effects of the heavy- and light-hole valence bands in GaAs