The electronic and optical properties of DyP and DyBi are investigated both experimentally and computationally. The reflectivity spectra, which have been measured up to 12 eV on single crystals, display richly peaked spectral structures that are analogous for both pnictides. From the measured reflectivities the plasma frequencies, Drude relaxation times, and optical conductivity spectra are derived. The fitted Drude conductivity reveals that DyP and DyBi are semimetals with a number of free carriers of about 0.16 and 0.23 per formula unit, respectively. The very-structured experimental optical conductivity spectra are compared to calculated spectra, which are computed using two different approaches to the Dy 4 f states: the open-core approach and the L͑S͒DAϩU approach in three versions. These approaches to the 4 f states lead to very similar optical spectra. There exists a reasonable agreement between calculation and experiment for a number of the spectral features, which are interpreted by specific interband transitions within the calculated band structure. The agreement between theory and experiment substantiates that the 4 f electrons do not participate in the bonding. The differences that remain between theory and experiment for some of the spectral features do not appear to rest on aspects of the treatment of the 4 f states, but rather to be intrinsic shortcomings in the description of the other band states.