No, you need to keep neutrals separate.
YOU CANNOT RUN SEPARATE CIRCUITS ON 14/3
That thing you're thinking of, is called a "multi-wire branch circuit" (singular). It is one circuit. Note that they share a neutral, and that's what makes them one circuit.
The only way you could conceivably ham-bone 2 circuits onto 14/3 is by using the ground wire as the second circuit's neutral, but that's so outrageously reckless that I mention it only to assassinate it.
Actually, you have a bigger prob^H^H^H^H challenge
Speaking of assassinating, I am assuming you will NOT be using one of those atrocious 6-8-10 circuit transfer switches that cost a fortune, aren't well built, are by shabby suppliers like FPE->Republic, cost 4 times as much, and have spaghetti wiring. Their only virtue is ease of retrofit, and that's no virtue at all on a ground-up rewire.
Generally the way smart people do it, is with a separate subpanel for the circuits to be switched between sources. Then you have a simple 2- or 3-pole transfer switch or interlock; this can be as simple as a $25 strap that ties together 2 backfed breakers in the panel. That, with a
And another alternative is DC power. For a modest "lights, refrigerator, few other things" supply, it may be better to "stay" in DC power, if your auxiliary source is battery plus solar/wind/microhydro/simple-gen. This avoids the significant energy overhead of an inverter running 24x7 merely to run loads that can work on DC. You can still use mains wiring and mains panels, however, the challenge I'm about to mention will become even bigger, because these systems must be rigidly separated from Mains.
When you are in auxiliary-power mode, or when switched to it, you will have two separately-derived power sources, and certainly, two separate panels. Because of this, wiring must be carefully separated, in particular, neutrals cannot cross. That means things like the 14/3 MWBC trick are right out.
In fact, you'll need a fan-light which has two separate neutral wires: one for fan and one for light.
Low voltage would need to be in different boxes or with listed partitions, and separate cables. If both sides are mains power, even if they're separate panels or sources, they can commingle in the same box or even the same cable. But still, neutrals need to be separated. And there's the trick. You need some way to "mark" which cable is coming from which service.
For instance, you could do a really diligent job of marking cables with colored tape (and leaving a bit past the cable clamp). (in particular, tape panel 2's white wires with gray tape). Or you could wire the alternate service in UF or MC cable instead of NM. Anything like that would be acceptable, but you'll need to do it, or you'll lose your mind trying to work inside boxes. I work in conduit and have as many as 4 circuits in a conduit at a time, and you have to color-code or you will make mistakes!