Noise from my headphones when I plug in my charging cable. Can you do anything about it?

When I use my headphones on my laptop and plug in my charging cable, I always hear a hissing noise. If I use a microphone, e.g. On the headset, then you can hear the background noise on the other line. Can you do something about it?

You could replace the power supply with one with less ripple and noise. Simple power supplies, as they come with many devices, very often do not output anything but a well-smoothed DC voltage.