Who was Rasheed in A Thousand Splendid Suns like in The Kite Runner and The Thorn Birds?

It can be argued that Rasheed's character most aligns with that of Mary Carson from The Thorn Birds and Assef from The Kite Runner.
All three share astounding similarities: they exhibit traits of megalomania and seem to suffer from what modern psychologists call narcissistic personality disorder.
Those who suffer from the disorder often display arrogant, cruel, and vindictive behavior. They have an elevated sense of self-importance and revel in exploiting others for their own gain or pleasure. Additionally, narcissistic personalities have a strong sense of entitlement: they expect others to capitulate to their will at all times. Their sensitive egos also contribute to a "persecution complex." When thwarted, they take the rejection personally; they must have constant praise, adulation, and acknowledgement of their phenomenal brilliance. Otherwise, they respond with insults, contempt, and bullying behavior.
Such personalities are also prone to envy, and they display little empathy for others.
I will argue that the above perfectly describes Rasheed, Assef, and Mary Carson.
Rasheed: Rasheed is definitely a textbook example of someone who suffers from narcissistic personality disorder. He requires absolute and impartial obedience from his wives. Rasheed revels in using physical force as a tool of control. He is lustful, vengeful, and cruel. Because of his narcissism, he imagines himself as a persecuted man when both Mariam and Laila team up against him. You are probably very familiar with Rasheed's story: he mercilessly beats Laila after suspecting her of adultery. However, in his delusion, he rationalizes his right to enjoy pornographic magazines. Rasheed's behavior demonstrates an egregious sense of entitlement.
Assef: Assef is a villain from the very start. He exhibits contempt for weakness and crushes anyone who stands in his way. In his youth, he brutally rapes Hassan and revels in cruel behavior toward the younger boys. Later, his cruelty extends to Sohrab, Hassan's son, whom he makes his personal sexual slave. In his adult years, his cruel streak and overestimation of his own importance leads him to become a Taliban leader.
Assef's cruelty is clearly demonstrated in chapters 21 and 22. In chapter 21, Assef participates in the stoning of fellow Muslims he considers apostates. In chapter 22, his depravity is fully evident. He gloats to Amir that he participated in a pogrom against Hazaras at Mazar-i-Sharif. Assef has always believed Pashtuns to be superior to Hazaras and shows only exultant glee at the plight of the massacred tribe. Assef characterizes the deaths of Hazaras as "liberating" and an essential component of "God's work." In chapter 22, we also see how Assef has exploited Sohrab for his own craven pleasure.
Mary Carson: Consider Mary's interactions with Father Ralph de Bricassart. Mary lusts after the handsome priest but knows that he is beyond her grasp, both physically and mentally. Outwardly, she is alternately cloying and ascerbic towards him. In her delusion, she imagines that her display of coquettish behavior mimics elements of youth. For his part, Father de Bricassart is content to humor the older woman: after all, she is made of millions and is certainly a very influential parishioner.
While Mary enjoys the priest's superficial deference, it does nothing to quell her sexual desire. She is a realist, however, and understands that sexual union will never occur. Mary is thus content to trade witty repartees with the priest. This behavior persists until she suspects Father Ralph's partiality toward Meggie. Her ego is shattered, and bitter envy becomes the predominant emotion of her last days.
She plots revenge with every ounce of malignancy in her. In short, Mary sets a trap for Father Ralph in the will she leaves behind. On her last night on earth, she tells the priest:

If I'd been younger I'd have got you in a different way, Ralph. You'll never know how I've longed to throw thirty years of my life out the window. If the Devil had come to me and offered to buy my soul for the chance to be young again, I'd have sold it in a second, and not stupidly regretted the bargain like that old idiot Faust . . . Insufferable conceit! Inside that envelope lies the fate of your life and your soul. I must lose you to Meggie, but I've made sure she doesn't get you, either.

In her will, Mary admits that she could have killed Father Ralph for rejecting her sexual advances. Instead, she finds a better "reprisal": upon her death, all of her vast wealth will be bequeathed to the Catholic Church, and Father Ralph will administer her estate (as he sees fit) on behalf of the church. The trap is perfect. Father Ralph originally intended for Meggie to inherit the thirteen million pounds. However, Mary's new will puts the Church at his feet. In the end, Father Ralph falls for the "trap" and endures great misery. He struggles with his sexual desire for Meggie and his guilt at depriving her of her inheritance.
https://psychcentral.com/disorders/narcissistic-personality-disorder/

https://www.helpguide.org/articles/mental-disorders/narcissistic-personality-disorder.htm