I don't think there's an official term for that relationship. I'm guessing that you're talking about your step parent's children - the ones he or she had without your parent.
Even if you didn't have a half-brother, the children belonging to your step-parent would sort of be your "blended family" siblings, or maybe, sibling-though-marriage.
Then according to your description, there is not actual name for that relation ship. You can say you are a bit related. Or just say your halfbrother's halfbrother.
My half brother(leigh) is from my mum but not my dad and leighs half brother is from a different mum AND dad. So i think it is nothing but not to sure...??
if your dad has a child by another woman, or if your mother had another child by another man, in either situation the child would be your half sibling
There is no actual relation in that sense. You could class him as family because you have a mutual half brother but that's pretty much it =].
It depends with which parents. Like your dad with another lady's son (that being your half brother)?