  We theoretically study dissociative ionization of H$_2^+$ exposed to strong
linearly polarized few-cycle visible, near-infrared and midinfrared laser
pulses. We find rich energy-sharing structures in the combined electron and
nuclear kinetic energy spectra with features that are a priori at odds with
simple energy conservation arguments. We explain the structures as
interferences between wave packets released during different optical cycles,
and during the same optical cycle, respectively. Both inter- and intracycle
interference structures are clearly visible in the joint energy spectra. The
shapes of the interference structures depend on the dynamics leading to the
double continuum, and carry sub-femtosecond information.
