First off, where do you plug your headphones to?
if you plug them to the speakers/display plug, windows has no chance to change their behavior.
The feature of "mute speakers if headphone is plugged in" that goes with speakers that have headphone jack in them is their thing.
If on computer front panel, most of the sound cards mute speakers when headphone is plugged into front jack. This can often be changed in settings but as you said, you have tried and looked and it is not there.
Leaving possible choice of back panel connectors as option. If plugged in there, the sound card should either ask what device you plugged in. If it doesn't ask, your chances of separately muting one or other is pretty much shot since at that point, the...