The woman, who Italian newspapers are calling Anna, and her husband were one of four couples who were receiving IVF treatment on December 4 last year at the fertility unit of the Sandro Pertini hospital in the Italian capital.
They believed the treatment had been successful when the woman was found to be pregnant. But during a routine test to check for any genetic anomalies in the developing foetus, the shocking truth came to light.
The devastated couple were informed that the twins they are expecting do not share their 'genetic profile'.
The embryos are believed to belong to another of the women treated at the clinic, known only as Lia. Heartbreakingly, Lia miscarried after her own implantation, and Italian daily La Repubblica is reporting that the miscarried embryos belonged to Anna, who they say is now carrying Lia's twins.
"These babies are living inside me," Anna said in a statement made through her lawyer. "I had a human moment of horror when I found out that the embryos I was carrying belonged to another woman."
But she went on to reveal that she and her partner planned to go ahead with the pregnancy. "We decided that the pregnancy should continue. These are our values."
The centre has been temporarily closed and no embryo implantations will take place until an investigation has been conducted into the procedures used by the clinic in the run-up to the calamitous error.
Hospital officials were quick to stress that the blunder was an 'isolated event'. In a statement, local health director Vitaliano De Salazar hastened to assure couples who have used the clinic in the past that there was no cause for concern about the genetics of their own offspring.
Health minister Beatrice Lorenzin was unimpressed with the way the case has been handled. "We learnt about this incident from the newspapers," she said, adding that the ministry 'will be investigating' the clinic's practices.
A five-person commission has been formed to determine exactly what went wrong. But this will be cold comfort to the couple now faced with the reality that the babies they had so desperately wanted are not theirs.
"What will happen after [she] gives birth to the twins she is carrying?" lawyer Michele Ambrosini demanded, asking whether the pregnant woman was now to be considered 'a future mother or a rented womb'.