Florida Couple Keeping Baby That Isn't Theirs After IVF Screw-Up

A Florida couple who gave birth through IVF were shocked to learn the baby isn't genetically theirs ... but they still want to be her mother and father ... and they've struck a deal with the biological parents.

Here's the deal ... Tiffany Score and Steven Mills are suing Fertility Center of Orlando for allegedly implanting the wrong embryo. Tiffany gave birth to Shea Score Mills, who doesn't look like her or Steven.

Tiffany and Steven have finally reached a custody agreement with their daughter's biological parents, according to court documents obtained by PEOPLE ... six months after Tiffany gave birth. The filing says Tiffany and Steven retain their rights to continue as Shea's permanent custodial parents.

Tiffany and Steve announced in April they tracked down Shea's parents through genetic testing.

A representative for the couple told PEOPLE ... "Tiffany and Steve recognize the public interest in the details of their IVF experience, and they appreciate the role the news media has played in bringing them and Shea to the point where Shea's genetic parents were able to be identified and fears about Shea's future have been settled."

The rep continued ... "Tiffany and Steve are committed to respect the privacy concerns of Shea's genetic parents with whom they have begun and intend to continue to foster a relationship of friendship and trust. They are also committed to protecting Shea from harmful intrusion on her privacy."

Tiffany and Steve had produced and stored 3 viable embryos with Fertility Center of Orlando ... and are now transporting their remaining embryo to another facility, according to the court docs.