A memorial service for Huber was held on Wednesday evening in the Back of the Yards neighborhood in Chicago.
"It is an unbelievable. Who would expect a child at 20 to die of a flu?" Vickie Treat, Caitlin's mother.
"She went to the hospital with the flu a week ago Saturday and then she died the next Saturday," said Charles Huber, Caitlin's father.
On Wednesday evening, Caitlin's parents carried their 1-year-old granddaughter. They became grandparents for a second time when Caitlin's daughter Patricia was delivered c-section.
Huber lived in Chicago for about the last year. She grew up in Nebraska.
She was a 20-year-old mother with a world of future ahead of her. Huber was planning a wedding, about to have a baby and was planning to go back to school. Then she got sick.
Doctors diagnosed the H1N1 flu. Within days she was in a coma. Doctors performed a cesarean section to save the baby. She died a day later.
"She was an amazing girl. And she had plans, like going back to school," said Monica Rodriguez.
Rodriguez lived with her in Chicago and went to school with her at Boy's Town in Nebraska where Caitlin served as mayor and commander of the school's ROTC.
"I went to see her the day before she died, you know," said Rodriguez. "I thought she was like, she couldn't understand what I was saying."
Huber even got to meet Colin Powell on a trip to Washington, D.C. her senior year. She is the second Chicago resident to die of the H1N1 flu, the fourth in Illinois. Her baby girl, born three months premature, remains at U.I.C. Medical Center. Her family in Nebraska is devastated.
"Last time I talked to my sister she said she was trying to, like she could push stuff and walk behind it but she can't walk yet by herself," said Chas Huber, Caitlin's brother.
There is a memorial service for Caitlin's family Sunday in Nebraska and a memorial on Friday at Boy's Town in Omaha. In a statement from Boy's Town, they call her "a leader who will be greatly missed."
In addition to the newborn, she also had a 1-year-old daughter who will now live with relatives in Nebraska.
Illinois Department of Public Health spokeswoman Melaney Arnold says all four victims have had other medical problems.
The department has reported 1,268 confirmed cases of H1N1 flu in the state. Most cases have been in Chicago and suburban Cook County.
Three other Illinois deaths have been reported.
A 22-year-old Chicago man died May 24. The death of a female from northwest suburban Cook County was announced May 27. And a 42-year-old Kane County man died May 28.
The Chicago Department of Public Health says the most recent victim was admitted to the hospital May 23 with flu-like symptoms.
The Associated Press contributed to this report.