I also found suggestions to disable or disconnect the PC speaker, but that didn't make any difference either.
I've just tried installing the latest drivers, both downloaded from Gigabyte and directly from Realtek, but they don't do any good. I can't think of anything relevant that I've changed since getting the headphones. I've only had the headphones for a relatively short time, but I've only started to notice this even more recently. It's also much harder to hear when the noise reduction and amplifier on my headphones are turned off, but again it's still there. I can only barely hear the sound on my speakers if I turn the volume all the way up, but it's still there. The noise is louder when the sound card jack is set to 'headphones', but I still get interference to a lesser extent when it's set to 'line out'. It also happens even when the sound itself is muted.
It's mostly noticeable when there's not much happening sound-wise, e.g. I can also hear some interference when I minimise and maximise things in Windows. The buzzing only seems to happen when doing certain things, possibly when there's a heavy hard disk and CPU load - I can hear it when watching HD videos from the hard disk and while playing certain games. I'm using the built-in Realtek HD audio on my Gigabyte P35C-DS3R board, and my headphones are a pair of Audio-Technica ATH-ANC7s. Lately, I've been hearing an annoying buzzing noise when using my headphones.