A direct simultaneous detection of electron (e-) and positron (e+) bunches was successfully performed using wideband beam monitors and a detection system at the (e+) capture section of the SuperKEKB B-factory. The time intervals between the secondary-generated (e-) and (e+) bunches were measured to investigate their dynamical capture process. The results show that the time intervals were measured in the range of 20--280 ps on average, and the line-order switch of the (e-) and (e+) bunches and their dynamical phase-slip process in the axial direction were clearly observed as a function of the capture phase of accelerating structures. In this report, the dynamical capture and phase-slip process for the (e-) and(e+) bunches under the two-bunch acceleration scheme is described in detail. This study opens up a new window for direct observation of the (e-) and (e+) capture process at any present and future (e+) sources.