Thanks for the clarification.
According to your PC's specifications, it has a "Headphone/microphone port" on the front panel. This port is for devices with a P3 plug.
So if you plug in the headset on the front panel, you should be able to use the microphone and headphones simultaneously.
However, you will need to specify in the Audio Manager that comes with the driver that you have connected a headset.
Usually, the Audio Manager is hidden in the system tray next to the clock. On HP devices, it may be named "HP Audio".
Open the Audio Manager and look for your PC's connector settings. With the headset connected, click on the front panel connector and specify that you have a headset connected.