The absorption spectrum of polythiophene and its derivative poly(3-hexylthiophene) (P3HT) is usually described in terms of an intrachain exciton coupled to a single phonon mode. We show that this model is too simplistic for highly ordered, regioregular P3HT and that, analogous to the case of charged polarons in this material, interchain interactions must be taken into account to correctly describe the absorption spectrum. We show that the lowest energy feature in the p-p* region of the absorption spectrum is associated with an interchain absorption, the intensity of which is correlated with the degree of order in the polymer. Correspondingly, we show that the emission from P3HT also exhibits contributions from both interchain and intrachain states, in a manner similar to that recently shown for poly(phenylenevinylene). Having reinterpreted the physical origin of the features in the absorption and emission spectra of P3HT, we then model these spectra and show how they evolve as the degree of order in the polymer is changed by varying several physical parameters including temperature and regioregularity of the polymer.