There are several biblical references to the siblings of Jesus; however, for many centuries the Roman Catholic Church has taught that these so-called brothers and sisters of Jesus were cousins or close associates, and the Greek Church has taught that these were step-brothers and sisters from a former marriage of Joseph.
To begin with, let's look at the scriptural evidence for Jesus' siblings. First, we read in Mark 3.32 that on one occasion Jesus' family was concerned for his well-being and tried to get near him. A message was passed on to Jesus, "Your mother and your brothers are outside, asking for you." On another occasion when he was teaching in his hometown we read, "Where did this man get this wisdom and these mighty works? Is not this the carpenter's son? Is not his mother called Mary? And are not his brothers James and Joseph and Simon and Judas? And are not all his sisters with us?" (Matthew 13.54-56). Other passages that speak of Jesus' siblings include John 2.12, 7.3-5, Acts 1.14, and 1st Corinthians 9.5. It seems the evidence is fairly strong that Jesus had both brothers and sisters.
So why the aversion to Jesus having biological siblings? Apparently, the primary reason is because of a longtime tradition that Mary, the mother of Jesus, remained a virgin throughout her life. However, for this tradition to make any sense the brothers and sisters mentioned above must be explained away.
To do this, the Roman Church has argued that the terms "brothers" and "sisters" are generic words that indicate a close relationship with Jesus, but not necessarily a kinship. However, Jesus' response to those who brought him the message of his family's concern in Mark 3, the passage mentioned above, indicates Jesus recognized a difference between kinship and camaraderie: "And he replied, 'Who are my mother and my brothers?' And looking around on those who sat about him, he said, 'Here are my mother and my brothers! Whoever does the will of God is my brother, and sister, and mother'" (Mark 3.33-35).
Still, the tradition continues and thus the brothers and sisters must be accounted for somehow. As mentioned above, the Greek Church suggested that these brothers and sisters were Jesus' step-siblings born to Joseph prior to his betrothal to Mary. There is little that can be offered to disprove this notion, since the biblical writers have little interest in Mary's personal affairs beyond her motherhood of Jesus and so they do not mention anything of children she may or may not have bore following Jesus' birth. However, there is no good reason (outside of tradition) to assume Mary would not have had relations with her husband after the birth of Jesus. Indeed, Matthew 1.25 implies the married couple assumed a normal relationship following the birth of Jesus: "but [Joseph] knew her not until she had borne a son; and he called his name Jesus." The key word "until" implies Joseph "knew" her after the birth.
The Roman Church teaches that the named brothers and sisters of Jesus were cousins. They begin by explaining that of the four brothers mentioned in Matthew 13.55 two were apostles and two were simply associates of Jesus. However, in John 7.5 we read that "even his brothers did not believe in him"; thus it seems unlikely that Jesus' brothers would have become apostles. In any event, outside of tradition, there is no good reason for presuming these "siblings" were in actual fact cousins.
So, did Jesus have brothers and sisters? According to scripture, as it is written, the evidence seems to support a kinship with actual siblings. However, in the words of Jesus himself, his brothers and sisters are really all those who do the will of God.