A US woman and her husband are suing a fertility clinic they say implanted a stranger's baby, lawyers said on Monday.

According to the lawsuit, two California couples gave birth to each other's babies after a mix-up at a fertility clinic, and spent months raising children that weren't theirs before swapping the infants.

When Daphna and Alexander Cardinale first saw their child, conceived through IVF, they noticed the girl had jet-black hair and a much darker complexion than anyone in their family.

The Cardinales said that they then had immediate suspicions that the girl wasn't theirs.

They suppressed their doubts, however, because they fell in love with the baby and trusted the in vitro fertilization process and their doctors, Daphna said.

DNA test reveals results

A DNA test several months later revealed the girl born in September 2019 was not related to either of them, and they had been raising another couple's child.

The realization that she had been pregnant with another couple's baby, and that another woman had been carrying her child, caused enduring trauma, she said.

"I was overwhelmed by feelings of fear, betrayal, anger and heartbreak,'' Daphna said during a news conference with her husband. "I was robbed of the ability to carry my own child. I never had the opportunity to grow and bond with her during pregnancy, to feel her kick.''

Lawyers in Los Angeles said that two laboratories connected by one doctor switched the embryos of two entirely separate couples and implanted them in the wrong mothers.

The couples eventually met and worked through the courts to gain custody of their genetic children.

A 'heartbreaking' exchange

"The moment our... daughter was born should have been among the happiest of my life," Alexander Cardinale said.

"But I immediately felt shaken and confused as to why I didn't recognize her. "When the truth came to light, it made exchanging the children all the more heartbreaking," he said.

"Losing the birth child you know, for the genetic child that you don't know yet... a truly impossible nightmare."

The lawsuit accuses the Los Angeles-based California Center for Reproductive Health (CCRH) and its owner, Dr. Eliran Mor, of medical malpractice, breach of contract, negligence and fraud. The couple has also demanded a jury trial and seeks unspecified damages.

The two other parents involved in the alleged mix-up wish to remain anonymous and plan a similar lawsuit in the coming days, according to attorney Adam Wolf, who represents all four parents.

Mix-ups like this are very rare. In 2019 a couple from Glendale, California, sued a separate fertility clinic, claiming their embryo was mistakenly implanted in a New York woman, who gave birth to their son as well as a second boy belonging to another couple.