The hypostatic union is the term used to describe how God the Son, Jesus Christ, took on a human nature, yet remained fully God at the same time. Jesus always had been God (John 8:58, 10:30), but at the incarnation Jesus became a human being (John 1:14). The addition of the human nature to the divine nature is Jesus, the God-man. This is the hypostatic union, Jesus Christ, one Person, fully God and fully man.
Jesus' two natures, human and divine, are inseparable. Jesus will forever be the God-man, fully God and fully human, two distinct natures in one Person. Jesus' humanity and divinity are not mixed, but are united without loss of separate identity. Jesus sometimes operated with the limitations of humanity (John 4:6, 19:28) and other times in the power of His deity (John 11:43; Matthew 14:18-21). In both, Jesus' actions were from His one Person. Jesus had two natures, but only one personality.
DO YOU UNDERSTAND NOW
And the Blessed Virgin Mary gave birth to Jesus, not just the flesh, but also the God....whicch we know as the hypostatic union each. Thus the Blessed Mary is the mother of Jesus of the flesh, and mother of God, known as the hypostatic union of each.
You cannot seperate Jesus into two. You said it yourself.