There are many ironies in the Da Vinci Code. Let me name a few of them for you.
First, perhaps the greatest irony in the whole book is that the church is the irreligious organization and the secular people like the Harvard professor, Robert Langdon, are more religious. For example, he says to Sophie: "What really matters is what you believe."
Furthermore, as the book unfolds, it becomes clearer that the Catholic church has a great secret to hide and will go to all lengths to keep the secret. The church will lie, cheat, and even kill, if it has to. For example, Sophie speaks these words to Silas, who represents the church: "You believe in God? Your God doesn't forgive murderers... he burns them." This is irony at its best.
Second, people who seem honest and filled with integrity like Sir. Leigh Teabing prove to be duplicitous and really in charge of a vast conspiracy. This comes out very clearly as the novel progresses. Teabing is one of the great masterminds that is using Langdon. But at first, he comes off as a charming intellectual, who wants to help Sophie and Langdon.