CHICAGO — The adoption counselor caught Rebecca Bennett on her cellphone and delivered an urgent message from the birth mother: “The baby is coming early. You have permission to be at the hospital. Go quickly. Go now!”

It was the day last June when Bennett and her husband, Joshua, were scheduled to have their second meeting with the 35-year-old Chicago woman who had chosen them — from among dozens of couples — to adopt her baby. They were planning to discuss the child’s name, visiting rights and other important details.

But medical complications brought the 4-pound boy into the world two months early, thrusting the Bennetts into a premature-birth adoption that, experts say, happens more often than might be expected.

About one in every eight adoptions starts in a neonatal intensive care unit, according to the Cradle, the Evanston, Ill., agency that facilitated the adoption. The numbers mirror the rate of premature births in the state and country.

And just as medical complications vary from one premature birth to another, the way adoptions unfold after a baby is born prematurely also differ in every situation — so much so that the Cradle requires all prospective parents to attend a workshop focused on adopting at-risk children.

This Christmas, just days after their son’s adoption became official, the Bennetts considered the thriving Atticus their greatest gift of all. The birth and adoptive families are grateful for the unlikely friendship they now share after months taking turns by the newborn’s incubator, exchanging text and email messages about his progress and handing off bottles of breast milk.

“There were a thousand times where I wanted to say, ‘Wow. We just did a really good job with a completely awkward conversation,’ ” said Rebecca Bennett. “We just pulled together and got to know each other while we were pulling for Atticus.”

Rebecca and Josh Bennett of Evanston, Ill., both 35, were used to things coming later, not earlier, than expected.

The couple married in 2004 and had planned to have children. But after years of infertility problems, they signed on with the Cradle in 2009.

Like other prospective parents hoping to adopt through the agency, the Bennetts prepared a handmade brochure describing themselves through photographs, stories and lists of quirky facts. The blue booklet tied with yellow ribbon described how Rebecca taught a music appreciation course at Northwestern University and how Josh had a successful career in marketing. There were pictures of each of them holding smiling babies. It also mentioned their love for roller derby and disdain for raw tomatoes.

The booklet was appealing enough that once a month, for a year, counselors from the agency called to say the Bennetts were finalists in a birth mother’s search for an adoptive family. But month after month, the child went to someone else.

“Each holiday, we’d go to parties where we’d leave and say to each other, ‘Next year, we’ll be here with a baby,’ ” said Rebecca Bennett. “And then the next year, we’d have the same conversation.”

The birth mother, who is not being named to protect her identity, is from the East Coast and began searching there for adoptive parents. At first, she thought it would be easier for the child to grow up far away from Chicago, where she became pregnant after an affair with a married man.

But as her pregnancy progressed, the idea of an open adoption, in which she could negotiate planned contact with the child, became more appealing.

When they met face to face, their conversation flowed so freely that the couple and the birth mother didn’t need the help of the facilitator assigned to the case.

In the car on the drive home, the birth mother felt certain that she didn’t need to meet anyone else.

“That’s it,” she recalled saying aloud. “They’re the ones.”

After the Bennetts learned they had been chosen to adopt Atticus, they forced themselves to remain cautiously excited. They knew they could be disappointed.

The birth mother “was trusting us with so much, with Atticus,” Rebecca Bennett said. “I kept reminding myself that the least I could do is trust back.”