Rectifying contacts have been utilized in the electrical characterization of Langmuir-Blodgett films of poly(3-hexylthiophene) mixed with stearic acid or 3-octadecanoylpyrrole. The current transport and the capacitive properties indicate that the Schottky barriers are thin and partially blocking because of relatively high dopant concentrations. Charge carriers can tunnel through the thin barriers making the transport bulk limited corresponding to Poole-Frenkel effect characteristics. Capacitance-voltage measurements reveal increasing dopant concentration with decreasing film thickness near the rectifying electrode. The frequency and thickness dependences of the capacitance and parallel resistance indicate that filament formation occurs during vacuum deposition of the top electrodes, and that these filaments extend deep into the polymer.