We report the collinear generation of white light pulses in bulk media by phase-locked and time-delayed intense laser pulses. The mutual phase coherence of the pump pulses is fully transferred to the two supercontinua, which thus show a highly-modulated two-pulse spectrum extending from all of the visible down to the near-infrared. We have investigated the effects of changing the relative delay between the pulses as well as the role of imbalances in the pump energy, and we have found that, at least in a limited energy interval, the mutual phase coherence of the two white-light pulses is surprisingly robust.