Sharing a neutral is called a "Multiwire Branch Circuit."

What you are talking about is fine as long as you have wired the receptacles such that the grounded conductor (that is, the neutral) is connected without using the device (in other words, pigtailed) and the handles on the breakers are tied together for both sides, you should be good for most versions of the code.

I have a similar question, and am a little confused by Ron's answer. I would like to power two circuits with 3 wires run through EMT: one neutral, and two (red and black) hots, which would go to adjacent but not tied-together breakers. My logic is that the current in the neutral would be lower than that in either of the hots, because they would be balanced; I don't understand why the breakers must be tied together. Of course, I could pull two separate neutrals, but would then lose the balanced circuit advantage.

Inspectapedia

This link provides a decent explanation of the need for tied breakers.

Randy's article explains the details more than I wanted to dive in on them. The handle tie for MWBS has some conditions which vary with code version, but frankly, you'd be safer to comply with it.

Mtvhike, the hots must be on different phases in the panel to safely share a neutral

That's what I meant when I said "adjacent breakers".