Two major arguments atheists use against the Bible are that it is ambiguous and that it is contradictory. A contradiction is when two opposing statements are said to be true in the same sense at the same time. But ambiguity is an inability to determine the sense or time in which a statement is said to be true. Therefore if the Bible is ambiguous, it cannot be contradictory, and if it is contradictory, it cannot be ambiguous. The reality is that the Bible is neither ambiguous nor contradictory.
The main way atheists argue that it is ambiguous is pointing to the different denominations of Christianity that exist. But just because a denomination exists does not mean it is valid. In reality, each denomination has varying degrees of accuracy in different areas, with some disagreeing only in minor areas, and others being provably heretical.
As an example of the latter, many people consider Mormonism a Christian denomination, yet Mormonism is a henotheistic (belief in many gods but focus on one) religion. Official Mormon teaching is that God was once a man on another planet serving another god, and that by obeying God, we can one day become gods ourselves. (1) But go and read Isaiah 43:10, where God calls on Isaiah as His witness that there were no gods before Him, nor shall there be after Him. If the Bible preaches that there are no gods either before or after God, yet Mormonism teaches gods both before and after God, the obvious conclusion is that Mormonism is wrong, not that the Bible is ambiguous enough to give Mormons a henotheistic impression. The same applies to every other denomination in existence. It's not the Bible that's ambiguous, but rather it is mishandled.
The Bible itself, including Jesus, repeatedly affirms this concept. Even during the time of Christ, "wolves in sheep's clothing" existed, and have caused numerous heresies to creep into existing churches, or even create new ones. As an example, Luke writes in Acts 20:29-30 "For I know this, that after my departing shall grievous wolves enter in among you, not sparing the flock. Also of your own selves shall men arise, speaking perverse things, to draw away disciples after them." In other words, not only shall people come from outside the church to speak deception, but also from inside. So is a fake denomination really proof of ambiguity in the Bible, or is it just proof that the unambiguous warnings of heresy are very much correct?
But if the Bible is not ambiguous, what about accusations of contradictions? These don't hold water either. See, although the Bible isn't ambiguous, that doesn't mean it's impossible to twist. It is possible to make the Bible appear contradictory by misinterpretation. Using faulty translations also helps.
As an example of the former, take Abraham's justification. Was it by faith, or by works? You will remember how I defined contradiction as when two opposing statements are said to be true in the same sense at the same time. In the case of Abraham, he was justified before God by His faith, but he was justified before man by his works. James actually demonstrates this in the same chapter in which he speaks of Abraham's justification. In James 2:18, he says "show me your faith without your works, and I will show you my faith by my works." (Emphasis mine). Notice how God doesn't directly enter the equation here. James is talking about how to distinguish between the dead faith of a lazy man and the true faith of a Christian. Therefore, in context, Abraham was justified before God by his faith, and before man by his works.
As we've just seen, not only are two of the biggest arguments atheists use contradictory, but even if they were to settle for either one, they still fall short. The Bible is neither ambiguous nor contradictory. Atheism, by contrast, often hits the latter problem in its argumentation.
References
1. Lund, Gerald N. - Is President Lorenzo Snow’s oft-repeated statement—“As man now is, God once was; as God now is, man may be”—accepted as official doctrine by the Church? (link)