Is audio jack detection a software or hardware function or both?

The audio jack, Line-in jack and microphone jacks are part of the BIOS settings as are other devices on the motherboard. The BIOS loads as to provide information to the Operating System about what resources are available then the OS loads drivers and makes things available for the user. If using Add-in ISA [old], PCI or PCIe cards for things such as video/graphics cards, USB cards, Network cards, sound cards, etc., the BIOS may not see them so then it's up to loading drivers in the OS for it to work with them.

Sometimes a disc will accompany a motherboard which has drivers for the devices.

If I have difficulties with devices I boot to a Linux LiveDVD or USB Thumb drive, usually get at least a minimal support to see if they still work.

ellary said:

I have an older ASRock Fatality Z97 board and am using Microsoft's audio driver.

When I once had an audio problem and reverted to the MS sound card driver whilst investigating it, I found that my headphones were not detected.
Once I'd reinstalled the sound card's proper driver, headphones were once again detected.

Best of luck,
Denis