Lots! In the Halo universe, the Bible is humanity's incorrect interpretation and retelling of the events of Forerunner era. Here's one of the strongest examples.
In Genesis, God feels betrayed by His creations, namely humanity and its trespasses. God decides to cleanse Earth with the Great Flood, which is to kill all life and restore it to a clean slate. However, in order to preserve His creations, God instructs Noah to build an ark. In this ark, Noah is to take his family and two of every species. The ark will protect them from the flood, allowing Earth to repopulate once the flood subsides and the Earth is cleansed. Following the flood, God forms a bond with Noah, known as the Noahic Covenant, where He vows to never again flood the Earth and end all life.
Now, let's make a few translations:
- God = The Precursors
- Earth = The Universe
- Great Flood = The Flood
- Humanity (and their betrayal) = The Forerunners
- Noah = The Librarian
- Noah's Ark = The Ark
Then let's rewrite the biblical description above.
In the early years of the universe, the Precursors are betrayed by their creations, namely the Forerunners and their war. The Precursors decide to exact vengeance with the Flood. Cornered, the Forerunners build Halos, which are to kill all life in the Universe and restore it to a clean slate. However, in order to preserve life in the universe, the Librarian was to index every species and bring them to the Ark. The Ark will protect them from the Flood and the activation of the Halos, allowing the universe to repopulate once the Halos have fired and the universe is cleansed.
As you can see, there's a very clear parallel between the two creation stories. I don't see a connection between the Noahic Covenant and the Halo universe Covenant, but there are numerous other covenants in the Bible that may be the actual connection.
There's certainly a lot more that you can build from as well. For example, Gravemind is an all-powerful force of evil stemming from the Flood which stems from the Precursors. Satan is an all-powerful force of evil stemming originally from God and Heaven as the angel Lucifer. Master Chief's role as the self-sacrificing savior of humanity certainly has its role as a Jesus allegory.
Unfortunately I'm more familiar with biblical theology than I am with Halo lore, so I'm sure there are many, many things which I have missed, and I apologize if my Halo origin lore is somewhat off and oversimplified.