Baba did not accept responsibility for Hassan's birth, as he should have, but neither did he shun the boy.

Baba did not understand Amir or accept him when Amir was a child, but Baba tried to be a good father. He provided well for Amir, sending him to school, celebrating his birthdays, and teaching him right from wrong. Baba rejected organized religion, but he instilled in Amir a sense of ethics.

When the political regime changed in Afghanistan, Baba protected Amir and his future by smuggling him out of the country, at great peril. On one occasion, he acted with great courage, risking his life to save a young woman he did not know from being raped by a soldier. Amir always remembered his father's decency and bravery in protecting her. Baba was smart, courageous, and strong in managing to leave Afghanistan and establish a new life of freedom in California.

Once they began their new life in California, Baba worked hard, struggling to support Amir. His life of wealth, comfort, and influence was gone, but Baba never complained. All his efforts were directed toward Amir's future. He was determined his son would have an education and a better life.

When Amir fell in love, Baba understood his son's feelings and helped him win Soraya's hand in marriage, according to Afghani custom. Dying of cancer, Baba continued to work as long as he could, again without complaint. He faced his death with courage and dignity, growing close to Amir and Soraya before he died.

Baba was far from a perfect man, but he lived his life with integrity in many ways.

While there might be some disagreement about what makes a tragic hero, in my opinion, Baba is not a tragic hero.  He has some of the requisite elements, for example, being sometimes noble and sometimes virtuous. However, the most common understanding of the tragic hero is that he causes his own downfall because of a fatal flaw.  In The Kite Runner, this simply is not the case.  Baba certainly has flaws. For example, he clearly had an illicit relationship with Hassan's mother, and he is wrong for sending Ali and Hassan away.  However, what happens to Baba and Amir, that they must flee their home, does not really have all that much to do with any fatal flaw in Baba, but is, rather, the consequence of the politics of the country. The fact that he dies after having some good years repairing his relationship with Amir and knowing that Amir and his new wife will have a good life in America also tends to not make him a tragic hero.

I would argue there is a better case for Amir being a tragic hero.  He does have a fatal flaw, a kind of cowardice, which haunts him throughout the book until he finally grapples with it. Even then, his cowardice has cost him and many others considerably.