While Elizabeth dearly loves her father, despite his faults, and is his favorite, it is clear that she has no admiration for her mother.
Austen very clearly states that the relationship between Elizabeth and her mother is an estranged one. In fact, as Mrs. Bennet is leaving Netherfield after the ball, Austen describes Mrs. Bennet as thinking to herself about how pleased she was to be believing that Jane would soon be married to Mr. Bingley and living in Netherfield but that also Elizabeth would be married to Mr. Collins. Since "Elizabeth was least dear to her of all her children," she felt that Mr. Collins was "quite good enough for her" (Vol. 1, Ch. 18). Likewise, Elizabeth feels equal dislike for her mother. In fact, it is shown that Elizabeth is frequently humiliated by her mother's lack of social decorum. For example, Mrs. Bennet encourages Kitty's and Lydia's flirtation with the soldiers. Also, she is frequently saying ridiculous and socially improper things, such as, at the Netherfield ball, she loudly talks to Lady Lucas about the prospect of Jane marrying Bingley, right in Bingley's own home, well before an engagement has even been established.
In contrast to Mrs. Bennet, Elizabeth is Mr. Bennet's favorite, and Elizabeth shares the sentiment. Even in the very first chapter it is made clear that Elizabeth is Mr. Bennet's favorite daughter. He feels that Elizabeth is the only one of the Bennet women who actually has any sense and enough quickness of mind to match his own, as we see when he says, "They are all silly and ignorant like other girls; but Lizzy has something more of quickness than her sisters" (Vol. 1, Ch. 1). However, while she feels an equal amount of affection for her father, she can't help but notice his faults. His biggest fault is that he married a woman who was socially beneath him merely for her beauty, and she turned out to be a very stupid, crass, and ridiculous person who is raising their daughters to behave improperly. Elizabeth feels that he is sensitive enough of the dangers and intelligent enough to give them better guidance but instead has taken a laissez-faire attitude and prefers to laugh at his wife instead. Austen is speaking of his intelligence and how it could be put to better use in raising his daughters when she says that Elizabeth was "fully aware of the evils arising from so ill-judged a direction of talents; talents which rightly used, might at least have preserved the respectability of his daughters" (Vol. 2, Ch. 42). Therefore, while Elizabeth feels a great deal of mutual affection for her father, even her relationship with him is imperfect due to the character flaws she observes in him.