Electromagnetic Interference in Cable
A three-wire cable is not ideal for such a situation; if small amounts of power are needed, and the power is not switched or current-modulated, the return current in
the GROUND wire might be constant enough not to couple power noise into your signal, but the better solution is NOT to have a 'common' wire for those two functions.   Remember, the I*R voltage drop in this wire IS added to the signal.

So, a four-wire cable (and if there are connectors, those too have some
resistance, so use four-position connectors) will work better.   You can use common-mode
chokes on the signal-wire pair, and a true differential amplifier as the
signal receiver, so it will only have a 'ground' connection at ONE end,
and no ground-loop  pickup will result.   The twisting of the data-wire pair
will help reject B field (adjacent motors etc.) pickup, but (at some
extra expense) a coaxial cable will do even better.   If high voltages
were present, capacitive noise coupling to the twisted pair is likely,
and the coaxial cable is the best choice.

This is not an unusual situation, and conbination coaxial/wire-pair
cable is available commercially (Belden #549945, for instance), or
if you want something off-the-shelf, PC video cables (VGA) or S-video
cables (two coaxial pairs and overall shield) are readily available.
Assembling your own conductors is problematic, because an overall sheath
is usually required, and molded-on sheathing is preferred to wrapping
with lots of black tape...

There's no way to prevent radio pickup, but common-mode chokes can block it
from your receiver without hurting the difference signal that is detected.
Other RF filtering depends on your data frequencies being different from the
interfering signal, but is often required.