A thrilled Angelina Jolie and Billy Bob Thornton are making plans to adopt their second Cambodian baby!

And they hope to be cuddling the youngster soon — even though they’re embroiled in a heartbreaking red-tape nightmare involving their first adopted baby, Maddox. Angelina has him with her on a movie set in Africa, but the U.S. government won’t issue her a visa to bring the baby back to America.

“We’re going to get little Maddox a baby sister,” an upbeat and optimistic Billy Bob told pals.

As The ENQUIRER reported two weeks ago, 26-year-old Angelina and her husband got little Maddox through a legitimate adoption approved by Cambodian authorities.

But then they got trapped in a bureaucratic hell when the U.S. put a freeze on bringing Cambodian babies back to America.

The visa restriction is an attempt to stop the theft of and trafficking in Cambodian babies.

“Like hundreds of other frustrated adoptive parents, Ms. Jolie and Mr. Thornton are caught in a shut-off pipeline,” a U.S. Embassy spokesman in Phnom Penh, Cambodia, told The ENQUIRER. “Many of these Americans really deserve to be parents, and there are plenty of orphans in Cambodia who could benefit from having parents who will give them a good life. But we need to separate the good cases from the bad.”

As a result, late last year Uncle Sam stopped granting visas to Cambodian babies adopted from that war-ravaged country until its government passes legislation correcting the abuses.

But a confident Billy Bob vowed: “We’ll get this sorted out.”

The “Sling Blade” star added he’s already looking ahead to a second adoption.

“Angelina and I have already seen the baby girl the last time we were in Cambodia, and she’s adorable,” he told a source.

“She’s not a blood relative of Maddox, but she is an orphan, too.”

Billy Bob has done a surprising about-face by laying out the welcome mat for another child, disclosed the source.

The 46-year-old star — who already has two children with his previous wife Pietra plus a grown-up daughter — always said: “Three is enough,” according to the source.

“But when Angelina was in Cambodia, shooting ‘Lara Croft: Tomb Raider,’ she visited an orphanage and her heart was captured.

“Now Billy Bob’s two little boys back in Malibu are so excited. He says, ‘They can’t wait to see their new little brother — and sister, when we get her.’ “

Concluded the source: “This story is going to have a happy ending.”