How do I stop sharing call history between two iPhones?

My husband and I both just upgraded to iOS 8.3. Now I notice that if I have a missed call it shows up on his notice screen and all my calls show up in his recent call history (and vice versa).

Both phones don't ring and they don't need to be near each other or connected by Wi-Fi. We do share an iTunes account.

How do I stop sharing call history between the two phones?

If you are on the same Apple ID that is going to happen.
You can set up your own Apple ID, including @icloud.com email address for free and then link it with your husband's account for the purchasing of apps, music, etc., using Family Sharing

4 people in my household are on iDevices and each one has their own Apple ID or iCloud address...but it is all linked to one account and we use family sharing.

Just make sure your husband doesn't set it so that he has to "approve" every purchase you make! ;)

Looks like Apple added a feature called "Handoff" Turning that to off should stop call history from syncing. Settings --> General --> Handoff