It used to be common for children to piggyback on their parents' credit to buy a car. Now, according to an auto leasing company, the opposite is happening.

In California and Florida, whose unemployment and foreclosure rates are among the highest, parents are increasingly using their grown children's higher credit scores to lease cars, said Sergio Stiberman, the founder and CEO of Inc. in Aventura, Fla.

Nationwide, the company has tracked a 29% increase from two years ago in the number of middle-aged parents asking their children to co-sign for them on a car lease, he said.

Many of these adult borrowers can afford to take over a lease payment "but have issues qualifying for credit," Stiberman said, which is why they "have been turning to their children for help."

More often than not, it is the "child," aged 21 to 28 years old, who calls the leasing company on the parents' behalf and asks to co-sign the lease, he said.

Borrowers who have children as co-signers take over a lease payment of $399 a month, on average, with less than 18 months left on the contract and no down payment, he said