Calculations of the absorption coefficient for tunneling-split intersubband transitions in double quantum wells are presented and the line shape is analyzed as a function of the temperature and dopant concentration. The peaks in the absorption coefficient correspond to tunneling-split intersubband transitions resulting in the resonant absorption of light. The lower-energy absorption peak is induced by electron tunneling. This doublet structure accounts for the transitions between the tunneling-split originally degenerate ground-state subbands in the isolated quantum wells and corresponds to the transition from the Fermi edge of the lower tunneling-split subband and the transition to the Fermi edge of the upper tunneling-split subband. These two transitions are unresolved at low temperatures but become resolved at high temperatures. When the dopant charge density is increased, the absorption peak strength increases. It also brings out another unresolved absorption peak due to the transition between tunneling-split excited states. \textcopyright{} 1996 The American Physical Society.