The shape of the mid-IR absorption spectrum provides valuable information about the "hole" polaron coherence length in doped and undoped conjugated polymer films. In poly(3-hexylthiophene) (P3HT) films, the spectrum generally consists of a narrow, low-energy peak A (700-1000 cm^-1) followed by a much broader, higher-energy peak B (2500-5000 cm^-1). By using a theory based on the Holstein Hamiltonian for mobile holes in P3HT, the IR line-shape is successfully reproduced for several recently measured spectra recorded in doped and undoped films, confirming the association of an enhanced peak ratio (A/B) with extended polaron coherence. Emphasis is placed on the origin of components polarized along the intra- and interchain directions and their dependence on the spatial distribution of disorder as well as the position of the dopant relative to the π-stack. The model is further adapted to treat donor-acceptor copolymers where the local HOMO energy varies periodically from donor unit to acceptor unit. The calculated line shape for a diketopyrrolopyrrole-based copolymer agrees well with the recently measured spectrum.