In conventional Monte Carlo simulations of electron and hole transport in semiconductors, the possibility of electric-field induced interband transitions between scattering events is not taken into account. In this article we study the effects of interband transitions on the electron (or hole) velocity and on the distance traveled by the charge carrier. The resulting quantum velocity, defined as the expectation value of the velocity operator for a state which is a superposition of Bloch states, contains an average group velocity and a quantum interference term. We calculate these terms for two cases, namely, for a simple parameterized two-band k.p model and for hole motion in wurtzite GaN, and compare with the one-band group velocity used in the conventional Monte Carlo method. The results show that interband transitions around closely spaced energy bands, which may arise in crystals with relatively large unit cells, like wurtzite GaN and hexagonal and rhombohedral SiC polytypes, may have a major effect on the particle velocity and particle trajectory, and therefore constitute a major influence on, for instance, electrical breakdown.