The man and wife, who wish to remain anonymous, claim their lives have been devastated by suggestions of extra marital affairs.
In what is believed to the first case of its kind in the UK, they are seeking damages against the Belfast Health and Social Care Trust in a case expected to begin in September.
"I couldn't love my children more than if I had fathered them myself," the father said.
"They are gorgeous kids and I'd rather die than not have them, but this mistake has devastated our family and almost destroyed our marriage," he said.
"We can't go out together because people openly stare at us.
"My wife has been asked if she's had an affair with an Indian man on holiday. In public, she'll shrug it off. But in private, she's often in tears."
The 47-year-old businessman and his 46-year-old wife started treatment at the Regional Fertility Centre at Belfast's Royal Victoria Hospital in 1998.
Although they requested "white Caucasian" donor sperm, the woman was fertilised with "Caucasian cape coloured" sperm and gave birth to a dark-skinned boy, now aged 10.
The clinic apologised to the couple in October 2003 but the couple have fought a long protracted case for damages.