Scanning-tunneling spectroscopy experiments have been performed on conjugated polymer films and have been compared to a three-dimensional numerical model for charge injection and transport. It is found that field enhancement near the tip apex leads to significant changes in the injected current, which can amount to more than an order of magnitude, and can even change the polarity of the dominant charge carrier. As a direct consequence, the single-particle band gap and band alignment of the organic material can be directly obtained from tip height-voltage (z-V) curves, provided that the tip has a sufficiently sharp apex.