He should not be both brother and half-brother of Sarah. That results from a parent conflict on Sarah.
One could also ask whether he was her brother or half-brother at all. I look at that section of the 'Biblical Tree' and find the vast majority of the names there are not to be found in the Bible. I have given up on trying to reconcile relationships there. Instead I leave that to those who would claim to have infinitely more expertise in marrying together myriads of different traditions and stories than I would ever claim to be able to do.
Private User,
I'm aware of the "Midrash" in Sanhedrin 69b, but
1) almost always prefer the earlier source, and more importantly
2) claiming that Sarah is Isca, and thus daughter of Haran, niece to Abraham, does NOT make sense. We know that Sarah was 10 years younger than Abraham, so trying to fit another whole generation between them... not very likely!
I have fixed the parent conflict for Sarah.