I know what you're describing, and I'm fairly sure I've seen such a thing done before in various movies or TV shows (although I'm struggling to name any...), so it's definitely a thing that's been done in various media before, in order to tell multiple sides/experiences of the same events.
My only hesitation is that, if you're writing it as a novel, you'll have to be very clear about the events/people/etc, make sure it's clear that it's the same story told from someone else's point of view, because you don't have any visuals to help. (Then again, I'm a comic artist, so I may be biased toward visuals.)