One of you will need to make an appleID (appleid.apple.com).
1) Go into settings > messages on the persons phone you chose to make the appleID for.
2) Tap on send/recieve.
3) Tap on "Use appleID for imsg"
4) Enter new "AppleID".
5) Make sure the old appleID list below (the one you share for itunes purchases) isn't check marked.
Settings>Messages>Send & Receive...edit here.
You can continue to share the same Apple ID for iTunes content, but one of you really needs to get an ID for iMessage, FaceTime, iCloud, Find My Phone, etc. Must be a verified email address. You can create an Apple ID here: