Cisco AnyConnect prevents Continuity from allowing Mac to answer iPhone

One of the nicest features of the new OS integration between iOS 8 and Yosemite is the ability to text and receive phone calls from my iPhone while on my Mac.

However, when I work from home, I need to use Cisco AnyConnect to create a VPN network. When the VPN network is active, I can see phone calls from my iPhone on my Mac, but answering the call on my Mac will cause the call to disconnect. Trying to call from my Mac will show the dialog box that I am connecting, but the iPhone never responds. If I am on a call on my Mac, and start up the VPN, the call disconnects.

I have a 2014 13" MacBook Pro and an iPhone 5S both running the latest OS with all the patches.

What is going on, and is there a way to fix the problem?