Microscopic analysis of intraband radiation absorption by holes with their transition to the spin-split band for InAsSb/AlSb and InGaAsP/InP semiconductor quantum wells is performed in the context of the four-band Kane model. The calculation is performed for two incident-radiation polarizations: along the crystal-growth axis and in the quantum-well plane. It is demonstrated that absorption with transition to the discrete spectrum of spin-split holes has a higher intensity than absorption with transitions to the continuous spectrum. The dependences of the intraband absorption coefficient on temperature, hole density, and quantum- well width are thoroughly analyzed. It is shown that intraband radiation absorption can be the main mechanism of internal radiation losses in lasers based on quantum wells.