This episode focuses narrowly on the explanation of John 8:56, in which Christ notes that Abraham "rejoiced to see My day and was glad." The explanation is very pertinent to the question, "Do Jews and Christians believe in the same God?" For if the father of Judaism, Abraham, actually saw the pre-incarnate Christ, in the context of making a covenant with Yahweh, then faith in God the Father is intimately linked with God the Son. Genesis 15:6-18 describes the covenant that God made with Abraham. When two parties made a covenant both would walk in between animals split in half, pronouncing blessings and curses for keeping the covenant. Abraham did not walk in between the animals but instead saw a "smoking oven and a flaming torch." When interpreted through the words of Christ, that Abraham SAW Christ's day and was glad, Abraham evidently saw his perfect representative, Christ, making a covenant with God the Father--good reason to rejoice. Abraham is described as "ungodly" in Romans 4:3, but is commended because he believes in God who justifies the ungodly. The Abrahamic covenant then anticipates the New Covenant that Christ instituted, in which ungodly men are justified by faith in Him. So even at the very beginning of Judaism, justification by faith in Christ, albeit not explicit, affirms the basis by which sinners approach a holy God, through a perfect representative. With respect to the question then, one can certainly say that Christians and the first Jew (Abraham) believed in the same God.
Who was the God of Jesus?
"This initial episode sets the stage for the question by asking ""who was the God of Jesus?"" All Jews were monotheists, daily reciting the shema, ""Here o Israel, the Lord Our God, the Lord is One."" Christ, a good Jew, affirmed this core belief of Judaism, but identified this God as His own Father, even claiming that He was the God of the Old Testament, citing the Name of God made known to Moses, ""I am that I am."" [YHWH} (Exodus 3:14, John 8:58) So, while the New Testament affirms that Jesus' God was Yahweh, it also describes the Trinitarian nature of the One God, Jesus being God the Son. Both God the Father and God the Son are one is essence, but distinct persons of the Godhead. John 1:1 consequently affirms the oneness of God described in the shema, but notes distinctions within the godhead, ""In the beginning was the Word, and the Word was with God and the Word was God."" Jews prior to Christ only had glimpses of this Trinitarian God in the Old Testament, for the explicit revelation of the godhead only came with the incarnate Christ, who ""explained"" the Father. (John 1:18)