You may both be signed in to the same Apple ID. If you each go to your iCloud or Messages settings, see what login is being used. If it is the same on both phones, that is your issue.
You can share the same iTunes ID. But you need separate iCloud, iMessage and Facetime ID's. Share only iTunes ID. That way you share the same purchases without paying twice. Also separate iCloud gives both of you 5 free gb of storage in iCloud.