Hi Kristinaoneal,
If your father is the account holder, he will have access to see everything on the plan that happens though a detailed bill. Now he won't be able to see the physical messages you send both email and text, just the number of the text and the amount of data that has been used. No account holder has access to see the body of the text messages unless they got on the physical device.
The only way to avoid him being able to see details on your usage would be to move off onto your own plan.
Hope this helps!