Line shapes of the R0(0) and R0(1) lines in the pure rotational band, and of the R1(0) and R1(1) lines in the fundamental band of HD are computed from first principles for HD molecules that interact collisionally with He atoms. Interference of the permanent dipole of the HD molecule and the interaction-induced dipole of HD–He supermolecular complex shapes these profiles. We use the close-coupling scheme for the scattering calculations which take into account the anisotropy of the HD–He interaction potential. Thus rotational level mixing is accounted for in a non-perturbative manner. The treatment is fully quantum mechanical and takes into account single binary collisions between HD and He. Spectral absorption profiles and line shape parameters of the R-lines are computed for comparison with existing measurements at 77 K. Agreement between theory and measurements is observed in the low-helium-density limit of the measured absorption as expected.