In order to get audio from your PC, your headphones need to be either plugged into the audio output of your PC directly, or plugged into something like your monitor that will pass the audio signal from your PC on to your headphones. So if you want to plug your headphones into your monitor for sound, then you need to make sure the monitor is plugged into the audio output port of your PC. Monitors with built-in speakers usually come with a stereo cable that will connect the PC's audio output (it's the green one if they are color-coded) to the monitor. Then the monitor either plays the sound out of built-in speakers, or it can pass the sound to a set of headphones or speakers when either is connected to the monitor.
So something has to...