But... his sister is my sister -__-
This cannot have a correct answer as you have not provided us with proper details. You said he has a different mother and both you and your sister share the same dad. So who is his dad and who is your mother?
However, if you mean he has a separate mom and dad from your parents, then that means you are in no way related to one another. Your mom and dad can be mom 1 and dad 1, his can be mom 2 and dad 2.
You are the son of mom 1 and dad 1. Your sister is the daughter of mom 2 and dad 1. He is son of mom 2 and dad 2. That means you have absolutely no biological relationship with him at all. However, the term brother doesn't have to mean blood relatives. My best friends are my brothers because I've known them for nearly my entire life. We were 3 when we met.