I have a half-brother and he has a son what does that make us and make him in my family?

That would be your nephew so you'd be his aunt/uncle

Your half-brothers son would be your nephew.

Half nephew

He us your nephew.

it makes you family

A half nephew. You have to decide which half.

First of all, in todays "blended families", it is not necessary to point out "less biological" relatives with "Half, Step or in-law" before or after their association to the immediate (or current) family. All this does is confuse children and belittle the person in question. Just consider that He is your brother, his son is your nephew, and if your parents are married, they are his Grandparents. Leave the hyphens to inquisitive strangers and just be family.