Jill Duggar is not giving up on her relationship with her father.

The pair have been estranged since she and her husband Derick Dillard distanced themselves from the TLC reality TV franchise that made her family famous beginning with "19 Kids and Counting." (TLC is owned by CNN's parent company).

"I always hold out hope. I mean, I think that with Christ, nothing's impossible," she told CNN. "So I hold out hope that one day our relationship will be in a much healthier place than it is even right now."

Jim Bob and Michelle Duggar starred in the reality series that showcased their large family and conservative religious beliefs as members of the Institute in Basic Life Principles, or IBLP. The Duggar parents were opposed to the use of birth control, promoted modest dress for the women in the family and had strict rules around courtship.

Jill Duggar has since broken from IBLP and put her energy toward efforts like her new book, "Counting the Cost," which she wrote with Dillard. In addition to the book being an opportunity to clear up common misconceptions about her and her family, Jill Duggar said her biggest motivation for writing it was to "be a voice for the voiceless."

Healing

"Counting the Cost," released earlier this month, speaks to both the financial and emotional cost of what the couple, married since 2014, say they have endured.

"My story is always being told for me," Jill Duggar told CNN. "Because I'm in the public eye and I grew up on television, people just assume that they have a right to my life. I beg to differ because I was a child whenever I was on television."

Duggar, 32, also starred in a "19 Kids and Counting" spinoff called "Jill & Jessa: Counting On" (later just "Counting On"), following the cancellation of the original show.

In a Prime Video docuseries, "Shiny, Happy People: Duggar Family Secrets,"Jill Duggar previously alleged that she and her siblings were not paid for their years as reality stars.

"I never received any payout—no check, no cash, no nothing," she said in the program.

Jill Duggar later spoke to People about how she and Dillard enlisted the aid of an attorney and eventually accepted a check from Jim Bob Duggar for $175,000.

CNN reached out to Jim Bob and Michelle Duggar for comment and did not receive a reply.

The parents previously told People in a statement: "Every family has differences of opinion and perspective at times, but families work things out. We all love Jill, Derick, and their boys very much. It is our prayer that our relationship is healed and fully restored quickly!"

There is much to be healed.

In 2015, the family reality show was canceled after reports that Josh Duggar, the family's eldest child, had molested girls as a teen, including two of his sisters, Jessa Seewald and Jill Duggar.

He was never charged in relation to those allegations.

In 2021, Josh Duggar was found guilty of receipt of child pornography and possession of child pornography.

He was sentenced in 2022 to 12 years in federal prison.

It's been a painful process for Jill Duggar, who shares three young sons with Dillard. She says she never wanted to be a public face for sex abuse survivors.

In the book, Jill Duggar opens up about the horror of having her experience go public and writes that she feels that her father has treated her brother better than her.

Through prayer and therapy, she and her husband, whose closeness was evident during the interview, are on a healing journey, they told CNN.

"When you're faced with obstacles and challenges, kind of like we were in our story, we had to choose," she said. "Are we going to choose each other? Are we gonna fight this together? Or are we going to let it tear us apart? And so that's like a positive where we chose each other and of course, relying on God."

Sorting it all out

Duggar's relationship with her siblings is complex.

"I kind of refrain from saying specifically who is like in our corner and who's still sorting things out. But other than just the positive feedback that I've had from one of my sisters, Jinger," she said. "She doesn't care that I say anything, but she's been very supportive and very positive. And then some of the other ones have been supportive behind closed doors. I just know for them and the space that they're in, they have to be careful."

She said she even attempted to send a holiday card to her brother Josh Duggar in prison, but it wasn't accepted. She theorizes that she's not on his list of those he can receive mail from.

She said she sometimes sees Josh's wife, Anna Duggar, at family functions and prays for her.

Josh and Anna Duggar are the parents of seven children.

Dillard supports his wife and desires to see her happy.

The death of his father in 2008 helped shape his faith, he said, leading him to think about the brevity of life. But at the same time Dillard said that he and his wife don't want people of faith "weaponizing the scripture and emotions" as they have witnessed.

"You don't want to be a travel agent for guilt trips and tell people, 'Well you you should come around and do what I need you to do because we don't know how much time we have and you just need to get in line,'" he said."We don't want to have a false sense healing either. I think that's been a big part of our journey, too -- realizing that we want true healing, not just faith healing."

Jill Duggar said it was also important in her book to let people know that it wasn't all bad and she does have some good memories of her time growing up. The struggles, she said, shouldn't invalidate "a lot of great memories" she has of her life and family.

"I think that you can have both memories and it's a lot like roses and thorns," Duggar said. "You can love the rosier parts of your story, but also recognize and process those more thorny parts."