You are looking for Jabra devices:
Wireless headsets with USB dongle and Bluetooth (for seamless mobile phone usage) or USB only Headsets. Look for the MS letters in their name - means Lync certified. Also check that your Jabra headset is supported by the Jabra Device Service (Tray Icon App).
That Jabra Setup does exaclty what you want: you can listen to regular audio while your audio communication is routed via your jabra device. Supports hotplugging: if no jabra device is attached, audio communication is routed via windows default setup for that.
The Jabra Device Service supports Lync, Skype, WebEx and serious list of regular softphones, such as Avaya, Bria and more. All simultaneously if required: first source that rings wins. It also knows if your headset is currently busy via bluetooth with your cell phone if eg a lync call comes in and acts accordingly.
Works like a charm with my Jabra Speakerphone (Desktop) and my Jabra Motion MS+ while travelling. I am using Lync, Skype, Avaya and WebEx.
Does not disturb listening to eg Spotify while calling.