You can mix them at the same time, but in the case of DCC power and signal getting to a DC motor, it ain't pretty. On Address "00" on a DCC hand-held, you will be able to run a single DC engine. If you place two or more on the tracks, they'll all behave as one, going forward or backward as they would on a DC track system. The real problem, depending on the condition of the drivetrain (motor, gears, and final drives) is that the DCC signal comes in a pulsed wave, which your DC motor will interpret as sounds from a squawking violin. The motor will 'sing' and groan, and sound like someone is pulling its nails out of its fingers.
The other way, a strictly DC layout with DCC engines equipped with decoders, is fine, although there are some caveats. First, you won't be able to fine tune the engines' performance, the whole rationale behind the decoders in the first place. Secondly, only decoders that are designed to run on both types of current (called 'dual mode' decoders) will safely operate on either type of voltage.
So, the idea of a two-way switch to enable power delivery by either/or is the way to go, and yes, keep both systems available to their proponents and adherents to maintain harmony. Those with dual mode decoders will have the better circumstances because they will be able to run their engines with more ease and no noise, but only if they can have access to the cabs controlling those engines' power districts.
-Crandell