Because the iPhone can receive an iMessage at either your phone number or an e-mail address, you're getting each others texts (iMessages only) because your iPhones are set to receive them at the same e-mail address. The same can apply to FaceTime ... if someone tries to reach you for FaceTime via your Apple ID e-mail address then you'll both get pinged.
You can easily fix this by either:
1- Create a new Apple ID for one of you, then go into Settings/ Messages and tap "Send & Receive" then tap the Apple ID at the top to log out, then log into the new Apple ID. By default, the iPhone will be able to receive iMessage at the Apple ID address. Note that using a new Apple ID does not affect iTunes purchases, you can share the same ID for that but use separate IDs for iMessage (and FaceTime).
2- (probably easier) Go into Settings/ Messages and tap "Send & Receive" then either de-select the e-mail address on one (or both) iPhones under "You can be reached by iMessage at:", and optionally add a different e-mail address to one of the iPhones.
Bottom line is that you need to not be sharing the same e-mail to receive iMessage and FaceTime requests.