Only a few authors have won both Newbery and Caldecott medals

I mentioned recently that William Steig was one of the few authors and illustrators to have won both Caldecott and Newbery medals. It's a short list. As far as I have been able to determine, only William Steig,Kevin Henkes, Holling Clancy Holling, Robert Lawson, Arnold Lobel, Ludwig Bemelmans, James Daugherty, and Alice Dalgliesh have won both awards. Just to clarify, the "honor" indicates a silver medal award for that year. The Caldecott is the medal for the most distinguished picture book, and the Newbery is for "the most distinguished children's book published in the previous year. (The award is limited to authors who are United States Citizens or who live in the United States, so you will never see Harry Potter on the list!) Some people say the Caldecott is the best picture book, and the Newbery is the best chapter book, but that is not always true. As you will note, Doctor De Soto, a picture book, won the Newbery medal.
The most recent to win both is Kevin Henkes, who won the Caldecott medal for Kitten's First Full Moonin 2005, won Newbery honors in 2004 for Olive's Ocean and in 1994 won Caldecott silver for Owen.
Holling wrote and illustrated a number of books including Paddle-To-The-Sea (Caldecott Honor) and Seabird (Newbery Honor).

Steig's Abel's Island and Doctor De Sotowon Newbery honors, while Sylvester and the Magic Pebble won Caldecott gold.

Robert Lawson won the Caldecott Medal in the 1941 for his family story They Were Strong and Good. In 1945, he won the Newbery Medal for Rabbit Hill. In 1958 he received Newbery honors for The Great Wheel (not currently in print).
Bemelmans won a Newbery honor for The Golden Basketwhich appears to be no longer in print. He won Caldecott honors for Madeline and the gold medal for Madeline's Rescue.
Alice Dalgliesh won a Caldecott honor for The Thanksgiving Story and THREE Newbery honors, for The Courage of Sarah Noble The Bears on Hemlock Mountain and The Silver Pencil.
James Daugherty won Newbery gold for Daniel Boone in 1940 and the Caldecott Honor in 1957 for Gillespie and the Guards--neither is in print now.
Many of these books and other medal-winning books, by other authors and illustrators, are still in print. I should caution you that for a few of the books that have won medals in the past, they were not books that have stood the test of time. Before telling your child to read all the medal books (as I've seen people do), I'd read reviews and see if the books still rank among the best books available for your child to read.