Structural irony is the type of irony that is built into the text throughout the story. It can usually be seen in the "naive hero" or the "naive narrator." The naive hero, or heroine is the one who thinks he/she understands things perfectly, but the narrator proves otherwise by the end of the story. In the case of the naive narrator, the reader understands things above and beyond what the narrator is saying. Jane Austen's Pride and Prejudice gives us an example of structural irony with respect to a naive hero/heroine.
One example of structural irony can be seen in Elizabeth's perception of Darcy. From the start of the novel, Elizabeth has already prejudicidely perceived Darcy to be a prideful man "devoid of every proper feeling" (Ch. 16, Vol. 3). In particular, at Netherfield, when Darcy says that "where there is a real superiority of mind, pride will be always under good regulation" Elizabeth hides a smile because she believes Darcy's pride to be highly unregulated (Ch. 11, Vol. 1). Later, we learn that the joke was actually on Elizabeth, because we learn that Darcy actually "has no improper pride" (Ch. 17, Vol. 3).
Also, because Elizabeth thinks Darcy to be without feeling, she completely fails to notice that Darcy is attracted to her and becoming increasingly so. Hence, we see structural irony play out when following the first ball at Meryton, at Lucas Lodge, Sir William Lucas tries to persuade Elizabeth to accept Darcy's request to dance. Elizabeth's response is to say "Mr. Darcy is all politeness" (Ch. 6, Vol. 1). This is a double joke. First, this line is an instance of verbal irony because Elizabeth does not think Darcy to be polite at all. But this is also structural irony because again the joke is on her. Elizabeth is wrong to assume that politeness is what is inducing Darcy to ask Elizabeth to dance. There are actually far deeper reasons that are beginning to bloom that the reader is aware of, namely he is becoming attracted to her. The reader first learns this when next Darcy tells Miss Bingley that he was thinking of Elizabeth's fine eyes.