If these are cables running between points where they receive and provide power, no problem. If they originate and/or terminate in the same electrical enclosure or box, all conductors must have insulation suitable for the highest voltage in that box or enclosure and there must be a partition between the conductors of different voltages.

Here is a link that might be useful: Partition

Actually...I seem to recall reading of some moronic (IMHO) new part of the code that prohibits low voltage and 120V wiring from going through the same framing penetration. The NEC seems to, at times, find the most outlandish/far fetched things that could happen and base code around them. Though my memory of reading about this one is different...I think it was just concern over interference. Well, interferance is never going to start a fire, so the NEC should just butt out. When I ran some audio lines through a hole in a joist that already had a 120V line, I use balanced audio connections and wires for this very reason. Interestingly even with very high quality Canares starquad cable, they still pick up just a tiny bit of 60hz hum that would otherwise not be there. Could have been mediocre CMRR at the receiving piece of equipment which was a cheap Chinese commercial sound reinforcement amplifier. (QSC brand...sounds pretty good though) Not everyone is going to put in a $100 set of transformers, certainly not on a budget piece of gear and so they usually just use an op-amp that costs 10 cents. Anyhow it's reasonable to infer that standard "RCA cable" would have been full of 60 hz hum. Still not a reason to outlaw it.

Thanks guys. I'm not real concerned whether it is code or not. Just if something bad is going to happen in a real world situation.

As far as interference goes, would this be intermittent or could I test the lights with various audio/video devices on,
to see if there's a problem?

"I seem to recall reading of some moronic (IMHO) new part of the code that prohibits low voltage and 120V wiring from going through the same framing penetration. The NEC seems to, at times, find the most outlandish/far fetched things that could happen and base code around them. Though my memory of reading about this one is different."
.Highly irresponsible to post such as this unless a specific reference can be cited. The post refers to lighting. Some equipment manufacturers do specify minimum spacing from other conductors, such as some NuTone intercoms.
For my part, the only reference I find in the NEC is Article 300.3 (C) (1) which completely disagrees with the quote from the other post.

Parallel runs of wire are prone to induced currents, especially in close proximity.

It is possible that the induced current overloads the conductor on which it was induced.

Nothing dangerous or unsafe will happen. I would try to keep a separation if the low voltage were for audio, phone, or computer simply from the standpoint of possible interference. But you should be fine for lighting.

"Highly irresponsible to post such as this unless a specific reference can be cited. "

Let me add some emphasis and rhetorical inference for you:

"I seem to recall reading of some [kind of]"

Of course I was being vague, because I knew someone else would probably come along who would be irritated enough to post a most extensive correction than they would otherwise have posted. Consider it a benevolent form of trolling hahaha. The attached linked discussion concerns mixed voltages in conduits and raceways, I have a vague memory of reading somewhere else that it now applied to something as brief as a framing penetration. Yes, I could be wrong about that (or the person whose post I recall reading).

Here is a link that might be useful: http://www.electriciantalk.com/f5/high-low-voltage-same-conduit-50817/

Since further schooling is required, the topic here is lighting. The (current) amperage for lighting at any voltage is far higher than any induced currents possible from 120 volt cables in a residence. Thus it is not a legitimate concern at all, unless falsely made to appear to be so.
Case in point, thermostat conductors for HVAC equipment are routinely run in proximity to the power conductors for that equipment without consequences. As is the control wiring for motor starters in industrial settings.at much higher voltages than 120.
Since the poster chose to research references to commentary about communication conductors but not the NEC 300, it is linked below.
Communication signals are a different matter.
It is better to not post than to misinform.

Here is a link that might be useful: NEC 300