Quantum dots (QDs) have promising optoelectronic properties. Colloidal QD heterostructures, systems in which two semiconductors are incorporated in a single colloid, may show novel and potentially useful transport phenomena. Here, we report on the physical mechanisms of charge transport through PbSe-CdSe core-shell QDs measured with cryogenic scanning tunneling spectroscopy. Compared to single-component QDs, an additional hole-induced electron tunneling channel is found. Electron tunneling with and without a hole occurs at different bias, allowing the determination of the electron-hole interaction energy (80 meV). This energy is sufficiently large to allow for a transport regime at room temperature in which electrons tunnel into the dot only if a hole is present, an ideal situation for controlled single-photon emission.