While a set of identical triplets is a rare enough occurence, one family's new bundles of joy are making headlines for an even more unlikely reason: Two of the three are conjoined at the lower abdomen.

The triplets, Catalina, Ximena and Scarlett were delivered via C-section one day short of 34 weeks on May 16 at Corpus Christi Medical Center, a release from the hospital said.

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All three each weighed 4 pounds, 11 ounces and were breathing without the assistance of a respirator, the hospital said.

When the couple found out they were expecting triplets and that two would be conjoined, mother Silvia Hernandez got emotional. "The truth is i cried, not because of how the babies would look ... I cried because the doctor said we had to understand and accept the fact that once they were born they could die," wrote Hernandez on a Facebook page started by the family

After the conjoined girls were transferred to Driscoll Children's Hospital in Corpus Christi, the babies' father, Raul Torres, told ABC News that he and his wife were relieved.

"We're good," he said. "The two babies are going into surgery right now. They're going to check their liquids to see that nothing's blocked up."

Torres told ABC News that the conjoined babies will likely be separated within six months to a year at Driscoll Children's Hospital.