Strong Shubnikov-de Haas (SdH) oscillations were observed in the derivative of microwave absorption () in InAs/GaSb/AlSb composite quantum wells (CQWs) using electron-paramagnetic resonance spectroscopy at low temperatures (2.7 to 20 K) and in the magnetic field up to 14 kOe. CQWs were grown on n-GaSb:Te(100) and n-InAs:Mn(100) substrates with various widths of QWs by MOVPE. A predominant contribution to the bulk n-GaSb substrate in SdH oscillations was manifested. Two frequencies of the SdH oscillations connected with warping of the Fermi surface of GaSb were found from Fourier analysis. An unusual angular indicatrix was observed in dependence on the orientation of the samples grown on n-GaSb in the magnetic field. The obtained results can be explained by bulk inversion asymmetry, which is a feature of substances with a lack of inversion centers. For CQWs grown on n-InAs:Mn substrate, only several SdH oscillations with higher period were observed. We succeeded in extracting a contribution of the two-dimensional carriers of InAs , where , from bulk substrate oscillations using a special spline interpolation from the angular dependence of SdH oscillatory amplitudes in the angle range of 0 to 90 deg.