We present a theoretical study of the electronic and nuclear flux densities of a vibrating H2 molecule after an electronic excitation by a short femtosecond laser pulse. The final state, a coherent superposition of the electronic ground state X1Σ+g and the electronic excited state B1Σ+u, evolves freely and permits the partition of the electronic flux density into two competing fluxes: the adiabatic and the transition flux density. The nature of the two fluxes allows us to identify two alternating dynamics of the electronic motion, occurring on the attosecond and the femtosecond time scales. In contradistinction to the adiabatic electronic flux density, the transition electronic flux density shows a dependence on the carrier-envelope phase of the laser field, encoding information of the interaction of the electrons with the electric field. Furthermore, the nuclear flux density displays multiple reversals, a quantum effect recently discovered by Manz et al. [J. Manz, J. F. Pérez-Torres, and Y. Yang, Phys. Rev. Lett. 111, 153004 (2013)], calling for investigation of the electronic flux density.