Using low-temperature scanning tunneling microscopy, detailed aspects of the charge density wave state in 2H-NbSe2 have been investigated by exploiting both the spectroscopic and topographic mode. The images are examined as a function of bias voltage and tip-to-surface distance. It is shown that the local density of states in the charge density wave phase is sensitive to the bias voltage, and especially to its sign, revealing the complexity of the electronic structure near the Fermi energy. In particular, for the first time a bias-dependent contrast in the charge density wave phase of 2H-NbSe2 was observed. This contrast must come from the spatial separation between the occupied and unoccupied electronic states responsible for the charge density wave.