In a previous answer, I argued that Baba was most like Fiona (Fee Cleary) in The Thorn Birds.
In this answer, I would like to present some evidence that Baba also shares some important similarities with Mary Carson in The Thorn Birds. First, both have a rather irreverent view of religion. They are also stubbornly independent, self-assured, and dominant. In her youth, Mary left Ireland and leveraged her beautiful face and figure to snag a wealthy husband in Australia. It is a point of pride for her that Michael Carson doted on her until the day he died. It's clear that Mary has always had an iron will and an indefatigable focus on her priorities.
In terms of religious preferences, Mary is Roman Catholic, while Baba is Muslim. Neither, however, has any illusions about priests or religious leaders. Here's what Mary Carson says about them:
"I must confess, Father, that this past year has been very pleasant," she said. "You're a far more satisfactory shepherd than old Father Kelly was, God rot his soul."
"I, too, think that there are more important things than lovers, but being a receptacle for God isn't one of them."
"Stuff and nonsense! You're here because of human failings—your own and the bishop's."
Mary is predominantly obsessed with preserving her power and influence in the society in which she lives. After her husband dies, she remains a widow, refusing to let either new suitors or priests decide her destiny in life. Baba is similarly independent in nature. Like Mary, he stubbornly refuses to bow to the spiritual authority of priests or holy men.
"Do you want to know what your father thinks about sin?"
"Then, I'll tell you," Baba said, "but first understand this, and understand it now, Amir: You'll never learn anything of value from those bearded idiots."
"You mean Mullah Fatiullah Khan?"
"I mean all of them. Piss on the beards of all those self-righteous monkeys."
Both Baba and Mary are pragmatic, shrewd individuals. They choose not to deny the lusts that beguile them, and they freely acknowledge the baser instincts of their nature. Mary openly lusts after Father de Bricassart, privately comparing him to an Adonis. Meanwhile, Baba has an affair with Sanaubar (his servant's wife). Both Baba and Mary are accustomed to getting what they want.
So, when Mary's overtures are consistently rebuffed by Father Ralph, she becomes bitter. Her bitterness grows into malice when she realizes that her beloved priest is drawn to Meggie Cleary. In the end, Mary uses her expansive wealth as a vehicle to torment Father Ralph for the rest of his life. She essentially betrays the man she claims to have loved and lusted after.
For his part, Baba also betrays those he claims to have loved: Sanaubar, Ali, and Hassan. After his affair with Sanaubar (which results in Hassan's birth), he neglects to recognize his illlegitimate son. Later, out of pride and social pressure, Baba lets Ali and Hassan leave his employ.
Similar to Baba and Mary, Jalil in A Thousand Splendid Suns also betrays the one who loves him. Sure, there are plenty of similarities between Baba (in The Kite Runner) and Nana in A Thousand Splendid Suns. Both have affairs that result in great suffering in their lives. However, Baba doesn't die in bitterness; Nana does. In that vein, Nana is similar to Mary Carson, who also dies with bitter malice in her heart. Before her death, she promises Father Ralph that she will make him sell himself like any "painted whore."
Back to Jalil. For his part, Jalil is one of Herat's wealthiest men. Despite his wealth, however, he succumbs to societal pressure and chooses not to recognize Mariam as his daughter. After Nana's death, Jalil gives in to his wives and chooses not to welcome Mariam into his household. Jalil's decision results in great suffering for Mariam, who ends up being married to the despicable Rasheed.
Having said the above, it is evident that Baba shares as many important similarities with Mary Carson and Jalil as he does with Fiona Cleary and Nana.