NEW YORK (NYTIMES) - Something did not seem quite right to Mrs Daphna Cardinale after she gave birth to her second child.

The baby girl, born on Sept 24, 2019, to Mrs Cardinale and her husband Alexander Cardinale through in-vitro fertilisation (IVF), did not look like them, the couple said. She had darker skin and jet-black hair.

For three months, the Cardinales raised the baby as their own, trying to rationalise the unexplainable. Their older daughter, who was five at the time, relished becoming a big sister.

But on Christmas Eve, the family said the "nightmare" became a reality: DNA tests confirmed that the Cardinales were not their baby's biological parents. When they confronted a Los Angeles-area fertility clinic about the results, they learnt that an embryo from another couple had been implanted in Mrs Cardinale and vice versa.

That New Year's Eve, the Cardinales finally met their biological daughter, Zoe, and they said they had taken custody of her about two weeks later in what they described as a traumatic exchange. They decided to keep Zoe's name.

Now, the couple is suing the clinic, the California Center for Reproductive Health, and its medical director in state Superior Court in Los Angeles County over the embryo "mix-up", which they said continues to haunt two families.

"We missed an entire year of our daughter's life," Mrs Cardinale, 43, said at a video news conference announcing the lawsuit. "We never saw our baby's entrance into the world or cuddled her in her first seconds of life.

"We had their baby and they had our baby," she said.

The law firm representing the Cardinales said it expected to file a similar lawsuit on behalf of the other couple, who was not identified in the Cardinales' lawsuit. The babies were born about a week apart.

The California Center for Reproductive Health and its medical director, Dr Eliran Mor, did not immediately respond to requests for comment. The website of the clinic describes Dr Mor as a reproductive endocrinologist.

IVF, an arduous path towards conception known for steep costs and at times painful treatments, involves stimulating a woman's ovaries to produce eggs with hormone injections and fertility medications. The eggs are then retrieved and fertilised with sperm in a laboratory before being implanted as an embryo into the uterus.

Peiffer Wolf Carr Kane & Conway, the law firm representing the Cardinales, estimated that the couple had paid US$50,000 (S$67,700) to the fertility clinic for the treatments.

In the lawsuit, the couple said Dr Mor had never disclosed that a third-party affiliate, In VitroTech Labs, would be used for IVF services and that Dr Mor was an owner of that business.

In VitroTech Labs and its parent company, Beverly Sunset Surgical Associates, are also named as defendants in the lawsuit, which accused the fertility clinic's operators of medical malpractice, negligence and breach of contract. In VitroTech Labs and Beverly Sunset Surgical Associates declined to comment on Tuesday.

Mr Cardinale, 41, said the most upsetting aspect of the ordeal had been breaking the news to their older daughter, who begged her parents to keep the baby. "How do you explain that to a five-year-old?" he said.

Mr Adam Wolf, a lawyer for the Cardinales, called during the news conference for tougher oversight of fertility clinics. IVF is a form of assisted reproductive technology, which is regulated by the Centers for Disease Control and Prevention, the Food and Drug Administration and the Centers for Medicare & Medicaid Services, according to the American Society for Reproductive Medicine.

"The Cardinales, you know, uncovered this relatively early because their baby was of a different race from them, but how many babies are there across the country who are of the same race but genetically unrelated to the people who used IVF?" he said.

In addition to emotional anguish, the couple said in the lawsuit that their careers had been adversely affected.

Mr Cardinale, a recording artist, was dropped by Atlantic Records after he could not promote his "then-hot" music single, the lawsuit said. He said: "We trusted people. How could this happen?"

Mrs Cardinale, a licensed therapist, lost most of the patients in her practice that she had spent years building, the lawsuit said.

"We came to it with incredible vulnerability and trust in our doctor and in the process," she said. "We had no idea at the time that this greatest potential for joy would bring us such enduring pain and trauma."

The couple said they continue to see the girl that Mrs Cardinale gave birth to and briefly raised, during visits with the other couple, who live near them in the Los Angeles area. "It's like," Mr Cardinale said, "how do you just become family with total strangers?"