We study mechanisms of absorption in two essentially different types of superconductor-insulator-normal metalinsulator-superconductor (SINIS) bolometers with absorber directly placed on Si wafer and with absorber suspended above the substrate. The figure of merit for quantum photon absorption is quantum efficiency equal to the number of detected electrons for one photon. The efficiency of absorption is dramatically dependent on phonon losses to substrate and electrodes, and electron energy losses to electrodes through tunnel junctions. The maximum quantum efficiency can approach n=hf/kT=160 at f=350 GHz T=0.1 K, and current responsivity dI/dP=e/kT in quantum gain bolometer case, contrary to photon counter mode with quantum efficiency of n=1 and responsivity dI/dP=e/hf. In experiments, we approach intrinsic quantum efficiency up to n=80 electrons per photon in bolometer with suspended absorber, contrary to quantum efficiency of about one for absorber on the substrate. In the case of suspended Cu and Pd absorber, Kapitsa resistance protect from power leak to Al electrodes.