The collision-induced dipole surface of an HD molecule interacting with an He atom is derived from the ab initio dipole data of the H-2-He complex [Gustafsson et al., J. Chem. Phys. 113, 3641, (2000)]. Collision-induced absorption spectra of gaseous mixtures of deuterium hydride and helium in the rotational and fundamental bands of HD are calculated, for comparison with an existing measurement taken at a temperature of 77 K. To that end, we integrate the close-coupled, radial Schrodinger equations, accounting for the anisotropy of the HD-He interaction potential. The computed absorption spectra generally agree reasonably well with the observed spectral profiles and intensities of the collision-induced spectra. We also consider the interference phenomena of the HD permanent dipole with the interaction-induced, supramolecular dipole by computing the wings of various R (j) lines and of the P-1(1) line in single, binary collision limit. For comparison, the line broadening and shift for the P and R line shape parameters are also computed using the impact approximation. The close-coupled treatment of our calculation of the spectral profiles accounts for rotational level mixing in a nonperturbative manner. The treatment is fully quantum-mechanical and takes into account single binary collisions of HD and He.