San Diego (CNN) -- A family rescued at sea with a sick baby is out of danger and back on dry land, but may be facing its toughest storm yet.
Eric and Charlotte Kaufman have been heavily criticized for taking their daughters, ages 1 and 3, with them on a sailing trip across the Pacific.
The 1-year-old, Lyra, became seriously ill hundreds of miles off Mexico, and the family had to be rescued.
"To our supporters and those who also seek an adventurous path with their families, we thank you for your kind words and support. From professional rescuers, professional sailors, and other families at sea we have been buoyed by your warmth and kindness," the parents wrote on their blogs Thursday.
"For those who are more critical, we ask that you kindly await all the details. There have been many inaccuracies reported through various media related to our daughter's health, the vessels' condition, and our overall maritime situation."
Exactly one week ago, the U.S. Coast Guard received a distress call about the girl, who was on the Rebel Heart with her parents and sister about 900 miles from Cabo San Lucas, Mexico.
Members of an Air National Guard unit operating out of Moffett Federal Airfield in the San Francisco Bay area were dispatched. Four members of the 129th Rescue Wing parachuted into the ocean, inflated a motorized boat and reached the 36-foot sailboat.
The crew of the USS Vandegrift picked up the family and the four rescuers.
The Vandegrift is a sophisticated warship with all the equipment and supplies necessary for a lengthy stay at sea. But one thing it doesn't stock is baby food. The crew stepped up.
"They went as far as making baby food. We made a makeshift crib. We did everything we could think of to try to get this family a safe place to recuperate," Lt. Cmdr. Daryl Robbin told reporters.
He declined to enter the fray around the parents' decision to set sail with young children in tow.
"It's not my position or my role to judge the people we rescue at sea. Just thankful we were able to get them back to the beach safely," he said.
According to their blogs, the Kaufmans had plans to cross the Pacific and left Mexico with their daughters Cora and Lyra. The family lives in San Diego, where they returned Wednesday.
They left there in 2012 and were slowly making their way around the world. In one of her earlier blog posts, dated October 2012, Charlotte said that she and her husband had done a ton of research and would never purposefully put their family in harm's way.
"Also remember that it is far, far more dangerous to drive every day on the freeway than it is to sail from San Diego to Mexico, or even around the world," Charlotte wrote.
Dan Simon reported from San Diego. Dana Ford reported and wrote from Atlanta.