Double doping, in which a single dopant molecule induces two charge carriers in an organic semiconductor (OSC), was recently experimentally observed and promises to enhance the efficiency of molecular doping. Here we present a theoretical investigation of p-type molecular double doping in a CN6-CP:bithiophene-thienothiophene OSC system. Our analysis is based on density functional theory (DFT) calculations for the electronic ground state. In a molecular complex with two OSC oligomers and one CN6-CP dopant molecule, we explicitly demonstrate double integer charge transfer and find the formation of two individual polarons on the OSC molecules and a dianion dopant molecule. We show that the vibrational modes and related infrared absorption spectrum of this complex can be traced back to those of the charged dopant and OSC molecules in their isolated forms. The near-infrared optical absorption spectrum calculated by time-dependent DFT shows features of both typical intramolecular polaron excitations and weak intermolecular charge transfer excitations associated with the doping-induced polaron states.