I haven't experienced it. So your SP3 behaves the same way when you plug in headphones while charging? Also I thought the Surface lineup used Wolfson chips which are supposed to be good. Or was that only in the Surface RT? Does anyone know what audio chips/DAC the Surface 2, Pro, Pro 2 and Pro 3 use?
Surface Pro 1 uses Realtek ALC3230
Surface Pro 2 uses Realtek ALC3230
Surface Pro 3 uses Realtek ALC3264
In my case, I can't really hear it. I can hear a continuous small hiss sound, but very very faint. I need to be in every quiet room to hear it when I plugged in. I can hear it, if I am on battery and turn off my desktop, but I noticed that it stops about less than 1 sec after music paused. I guess it's the sound chip that mutes to save power when no sound.
But using my desktop onboard sound chip, it's god awful. You hear the interference from just moving the cursor on the screen (which every desktop I ever had do this, even with motherboards that claims to use "premium" sound chip. It's fine for me, as I buy a sound card, and it lasts me several computer upgrades. I usually change it because of Windows drivers, or some jack broke, or I seek for a better sound.) As for my old laptop, well I didn't have my headphones then, but I can tell you, my 30$ ****ty emergency Sony headphones (others broke), it was horrible. I didn't hear the static using them, but the audio was exceptional horrible, but if I plug a stereo to it, you hear some heavy, like heavy, static, when plugged in. Not on battery. I didn't try on my Surface Pro 2, to be honest, so I don't know.
So, I don't know, in your case, if it's because of the sound chip, or the way it was implemented on the Pro 3 more tighter circuitry, or your headphones that is able to sensible enough to hear it (low impedance is the factor?! I don't know, I am guessing.)
It is the Surface 1(aka: RT) that has the Wolfson chip
All I can think about is the following:
-> Close nay running music program
-> Go to Windows sound option panel, and make sure that everything is muted as inputs (microphones/line in if any is there)
-> Double click on your headphones under the Playback tab. Another panel will show.
-> On that panel, go under the Advanced tab, and set the format to the highest quality, and hit Apply. You can close everything
-> Now try playing some music. Does that help a bit?