This is with iMessages only, not with regular text messages - SMS/MMS and means the same Apple ID was activated with iMessage on each iPhone. This is by design and intention when one person has more than one iOS device and/or Apple computer wanting to have all iMessages available on all devices. I can start an iMessage with my Mac at home, leave the house or leave my computer and continue the iMessage conversation on my iPhone or vice-versa with all my iMessage conversations available on my Mac, iPhone, and iPad.
You or your wife need to create another Apple ID to be used with iMessage on your iPhone. Sign out of the current shared Apple ID with iMessage on your iPhone or with your wife's iPhone followed by signing in with the new Apple ID. Do the same with FaceTime.
This will not affect Find My iPhone with the shared iCloud account on each iPhone and the same with the current shared Apple ID for the iTunes and App Store.