Why do the Jew study the orthodox Christian Bible?

Studying Torah-texts is something we are commanded to do (Deuteronomy 11).

• The Hebrew Bible:

The Tanakh (Hebrew Bible) is important because it tells the history of the ancient Israelites, as well as giving us the teachings of such prophets as Moses, Isaiah and Jeremiah, the stories of kings like David and Saul, and the ethics and beliefs of the Jewish religion.Our tradition is that the Hebrew Bible is from God (Exodus 24:12), given to us to provide knowledge, guidance, inspiration, awe and reverence, advice, law, comfort, history and more. It is the basis of Judaism. It crystallized, strengthened and codified our beliefs; insured our awareness and knowledge of our identity and history; and provided powerful impetus to be ethical.
It made us stand in awe of God, while also providing optimism and comfort through the prophecies of redemption. It inspired us to strive for holiness and informed us how to pray and to approach God's presence.
And it set detailed laws, practices and traditions for us forever.

Link: Israelite prophecy

• The Talmud:

Religious Jews live by the Torah, by obeying its commands and beliefs. There are hundreds of examples. However, the Torah "as is" isn't exactly what Judaism observes. Rather, It's the Torah together with the details provided in the Talmud, which is the Oral Law that was handed down together with the laws of Moses. Otherwise, the verses of the Torah often lack enough detail to be fulfilled as is.Link: Some examples of the Torah's commands
For instance, the law of honest weights and measures (Leviticus 19:36) does not state if any deviation is permitted. How often do the scales need calibration? What is the penalty for overcharging? Etc.

The laws (Deuteronomy ch.17) concerning the judges (Torah-sages; Sanhedrin) do not say what exactly constitutes bribery (Deuteronomy 16:19). Is it bribery if I compliment a judge before the court case but do not give a gift? And myriad other questions: How many judges are a quorum for Torah-courts? Is there a time limit for court cases? Etc.

The laws concerning restitution for damages (Exodus ch.22) do not tell us if payment needs to be made for emotional stress.

The key Hebrew Word in Exodus 22:4 can mean either fire or cattle. Which is it? Or is it both?

In Exodus 22:5, is there a difference in restitution between deliberate and accidental spreading of fire?

So the answer to your question is that the Torah (Hebrew scripture) summarizes our laws, while it is the function of the Talmud to expand upon the details, and to give us the precedents and Torah-tools for determining new cases in the future.

Link: More about the Talmud

Link: What is the problem with interpreting the Hebrew Bible literally