Someone who is misogynistic has a hatred or at least a significant disregard for women. Let's look at some the characters in Khaled Hosseini's A Thousand Splendid Suns and see if they show misogynistic tendencies.
We could certainly answer with a firm "yes" for Rasheed. He is horribly abusive toward his wives and clearly cares little for women in general. Notice how he treats Mariam and later Laila. Another misogynistic character is Mariam's father, Jalil. Think of how he treats his daughter, who is illegitimate. He marries her off with no regard for her preferences or safety.
On the other hand, Laila's father, Babi, wants his daughter to get an education and does not force her into marriage. He is seriously considering leaving Afghanistan so that the female members of his family will have better lives. Laila only ends up with Rasheed after her family is killed. You might also look at Laila's close friend, Tariq. He seems to be a man who loves deeply and treats people, including women, with respect. By the end of the book, he and Laila are together and working for the good of others.