There can be no half-brothers of half-sisters of JesusNo, the Bible did not say "sisters" or "brothers". That was King James. The original would have said 'male kin' and 'female kin'. This includes half brothers and sisters; step brothers and sisters; cousins (first, second, even third). Non-Catholic denominations prefer to believe 'male kin' were all brothers and 'female kin' were all sisters. Catholic/Orthodox belief is that they were not full siblings. To add to the Catholic/Orthodox point, care of the mother fell to the oldest son. Upon his death, care would fall to the second son. Yet, as he was dying on the cross, Jesus said to John and Mary, Behold your mother, behold your son--and it was John who took care of Mary from then on.
Also, the word around very early Christians (Apostolic tradition) was that Mary remained a virgin. Remember, these early Christians would have been Jews, and Mary's continued virginity would have been juicy gossip at the time, as this was unheard of for married women. In her own time, Mary never would have been admired for such a thing, she would have been scorned.
All of this has been laid out before. Personally, I could not care less what the situation was because we.do.not.know. We have two hypothesis and as neither can be proven, it silly to argue which is right. Again, we.do.not.know. And have no way of finding out. Let it be.