For organic solar cells (OSCs) based on nonplanar phthalocyanines, it has previously been reported that a thin film composed of triclinic crystals with face-on (or flat-lying)-oriented molecules, typically obtained with a CuI template layer, is desired for optical absorption in the near-infrared (NIR) spectral region. However, this work demonstrates that for a PbPc-C60 donor-acceptor pair, less face-on orientation with a broader orientation distribution obtained with a new template layer consisting of a ZnPc/CuI bilayer is more desirable in terms of solar cell efficiency than the face-on orientation. A NIR-sensitive PbPc-C60 OSC employing this bilayer-templated PbPc film is found to increase the internal quantum efficiency (IQE) by 36% on average in the NIR spectral region compared to a device using a CuI-templated PbPc film. Analyses of the change in IQE using the exciton diffusion model and the entropy- and disorder-driven charge-separation model suggest that the improved IQE is attributed to the facilitated dissociation of charge-transfer excitons as well as the reduction in exciton quenching near the indium tin oxide surface.