Sounds like he has the email address associated with your apple id set up to receive messages on his device. Go to settings>messages>send & receive and see what email addresses and phone numbers are associated with it. In order for him to receive your messages, your email address or phone number would have to be listed here.
Welcome to iMore! @cwbcpa is correct. He's receiving texts because you are sharing the same Apple ID. I recommend one of you set up a new one. You can always use family sharing to share purchased content like apps, movies, music, books, etc.
You can share the same iTunes ID. But the iCloud, iMessage and Facetime ID's should be your own. If it's just the 2 of you, sharing the same iTunes ID works great. It's what my wife and I do.