The four-member crew was among nine people, including the children's Australian mother, Sally Faulkner, who were arrested over the incident last Wednesday.
Surveillance video purportedly shows the moment members of a so-called child recovery agency snatched the children, Lahlea, 6 and Noah, 4, from a Beirut street.
Lebanese police says the children were later found and returned their father, Ali al Amin, who, according to Faulkner, took their children from Australia to Lebanon and refused to return them.
According to the Nine Network, the crew is facing charges including hiding information, forming an association of two or more people to commit crime against a person, kidnapping or holding a minor even with their approval, and physical assault.
The charges carry possible jail sentences ranging from three to 20 years, the network said on its website.
The film crew -- including reporter Tara Brown, producer Stephen Rice, cameraman Ben Williamson and sound recordist David Ballment -- had been in Lebanon to cover the story of Faulkner's attempts to recover her children.
A Nine Network spokeswoman declined to comment on Australian media reports that the broadcaster had been involved in setting up payments to a child recovery service involved in the alleged kidnapping.
"We're not making any comment about payment -- we don't ever make any comment about payment."
The spokeswoman added: "They're journalists covering a story -- that's all."
Faulkner has mounted a months-long campaign to push for the return of her children.
In a change.org petition posted last year
, Faulkner pleaded with Australian Foreign Minister Julie Bishop to intervene in the case.
"They were terrifyingly put on a plane by my ex-husband and I haven't heard from them since," Faulkner said in the petition, which attracted more than 33,000 signatures.
Bishop said consular officials had met with the detained crew and were providing assistance.