Jane Austen's works can actually be classified as an unusual mix of both realism and romanticism. While her novels certainly reflect real-life situations, her hero is actually a cross between a realist and romantic hero and so are her endings.
At first, neither the reader nor Elizabeth actually like Mr. Darcy. We agree with Elizabeth when she finds him "proud, to be above his company, and above being pleased" (Ch. 3). This characterization of Darcy is certainly very realistic. It is also very realistic that a quiet reserve such as Darcy has can be easily mistaken for excessive pride. However, what makes him more of a romantic hero than a realistic one is that he is also described as being a "fine, tall person, [with] handsome features, [and a] noble mien" (Ch. 3). In addition, he's very wealthy. While men like that certainly do exist in the real world, it is not very often that one meets with them. Therefore, Darcy's description of good looks, wealth, and noble mind make him more fitting of a romantic hero. In addition, like a romantic hero, Darcy is responsible for rescuing Elizabeth as well as the entire Bennet family. When Lydia runs off with Wickham, it is Darcy who bribes Wickham into marrying her. Lydia's actions would have ruined, not only her own reputation, but the reputation of the entire Bennet family. When Elizabeth thanks Darcy for his kindness, he replies, like a romantic hero, "If you will thank me ... let it be for yourself alone ... your family owe me nothing. Much as I respect them, I believe I thought only of you" (Ch. 58).
A second way in which Austen's realist novel digresses into a romantic novel is with respect to the happy endings. A realist novel is certainly entitled to having as happy an ending as any romantic novel. Realist novels must always end with a sense of closure in that the issues relayed in the book must always be either resolved or dissolved. However, where realist and romantic novels diverge is that, while the ending of a realist novel can be happy, it will also underscore any moral or political reason that created the novel's conflict in the first place ("Realism and the Realist Novel"). For example, Pride and Prejudice discusses the effects of improper behavior due to poor breeding. As part of the ending, not only does Elizabeth marry Darcy, but both Elizabeth and her father realize the errors of their family's ways. Therefore, since the ending of Pride and Prejudice ties back to morals rather than just being an ending about marriage, it is indeed a realist ending.
However, ways in which the ending is more romantic than realist is that the ending is almost too happy. One instance is seen in the case of Lydia's marriage. While it is possible that Wickham could have been bribed into marrying Lydia, another realistic scenario is that Wickham abandons her and leaves her to the consequences of being a fallen woman. So, since Darcy the hero saves the day, it is also a romantic ending.