Given the state of Bluetooth you're not going to find that kind of earpiece any time soon.
Going bi-direction requires having a base point for the device to connect with. You're not going to find one that will have enough range to cover a whole house. Nor are you going to find one that's got enough smarts in it to understand how to automatically roam between different bases and headsets. Don't forget fidelity, most headsets aren't engineered for much bandwidth, making them a poor choice for music.
And then there's the problem of battery size, nothing that had all those features (if they existed) would be small enough to wear comfortably.
The final nail in the coffin is target market, there's just not enough people out there that would want/need such a thing as to justify making it, let alone get to economies of scale that make it affordable.
So, step back, what is it the customer thinks they want to do? Be constantly yammering on the phone while walking all over the house, but ready to hear a doorbell or listen to music all at the same time?
A telephone system using cordless handsets would be able to integrate with a door intercom pretty easily. Background audio through in-wall speakers would handle most music situations. One with wall-mounted controls would eliminate the fumbling-around-for-a-remote hassle when they need to silence it. You can often integrate doorbell or intercom notification into them too (not bidirectionally though). Most modern cordless phone setups can handle up to 10 handsets, so that'd cover most houses.
Otherwise the closest they come to making it work would be using a regular cell phone with a bluetooth headset and some phone system features to handle forwarding calls from the house (for the intercom/doorbell) out to the cell phone. But then they're stuck walking around with the cell phone, and headset and keeping them charged all the time.
So, what's the real driving influence here? Because you're not going to find everything all together in one setup. What need gets the greatest priority? That'll drive the solution choice.