Hi,
The MSO54 is not capable of doing two independent timebases, but it is capable of recording 80 ms of events at the full 6.25 GS/s, which would allow you to record both of your events at the same time and then zoom in on the event you would like, with no loss of signal fidelity. Higher recording lengths are possible with lower sample rates.
The image attached displays such a setup. Please note the Horizontal menu.