Orthodox Christian theology has decisively rejected the idea that Jesus Christ is a demigod in this sense. At the Council of Chalcedon in 451 a definition of the faith was agreed with the following words about the two natures of Christ:
one and the same Christ, Son, Lord, Only-begotten, recognized in two natures, without confusion, without change, without division, without separation; the distinction of natures being in no way annulled by the union, but rather the characteristics of each nature being preserved and coming together to form one person and subsistence, not as parted or separated into two persons, but one and the same Son and Only-begotten God the Word, Lord Jesus Christ
In other words, Jesus is not half divine and half human, but fully God and fully man, without any kind of confusion or change in the natures, while also being one person.
While this definition does not explicitly rule out the idea that God the Father or the Holy Spirit took the role of a human father in the conception of Jesus, it certainly makes it more difficult to hold. Christians have often been accused of believing that Jesus is the product of a sexual union between God and Mary, but this has never been orthodox belief. I would conclude (along with John Robinson and Arthur Peacocke) that this Chalcedonian definition tends to support, without actually requiring, the kind of controversial explanation of Jesus’ virgin birth which I put forward yesterday.