The term Hypostatic Union is used in some Christian theology to describe the presence of both human and divine natures in Jesus Christ. It became an 'official doctrine' at the Council of Chalcedon, which stated that the two natures (divine and human) are united in the one person of Christ. This term is derived from the Greek word 'hypostasis,' which literally means to stand under. It is translated 'substance' in Hebrews 11:1.
The implication of standing under something is that the hypostasis is the true substance or essence of a thing. When it comes to understanding Jesus Christ, the idea is that the true essense of Christ is that He is both deity and humanity united in a single being. Some interpret this to mean that God died on the cross. As you have noted, Acts 20:28 describes the blood of Christ as 'God's own' blood. So how is this to be understood? First, when we think of God in the sense of His Deity, we know that God is Spirit (John 4:24). As Spirit God is invisible and eternal. In this regard, God cannot die. He is eternal. But we also know that in the fulness of time, God took on humanity, which like all humanity was visible and mortal. This humanity we know to be Jesus Christ, the Son of God. But we also know that this humanity was God Himself, manifested in the flesh. So when we speak of the one who died on the cross, we can say that God died in the flesh; that is, His humanity died. But to avoid confusion, we would not normally say that God died, since Spirit is eternal. It was only the flesh of God that died, was buried, and rose again the third day.