flat daddy
n. An enlarged, usually life-sized photograph of a deployed soldier, used to comfort that soldier's children, spouse, or relatives.
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To make your daughter feel good at home, you can tape your husband as he reads books to her and then play one of those tapes after he leaves, while she holds the book. You can make a "flat daddy" for her, too, by having a big enlargement made of your husband's picture and hanging it on her bedroom door or sitting it in your husband's chair at dinnertime. You can even have his picture scanned on her pillow.

The "flat daddy" idea is one of many good suggestions made by the National Military Family Association.
—Marguerite Kelly, “How a Dad Can Be in Two Places at Once,” The Washington Post, September 08, 2006
Maine National Guard members in Iraq and Afghanistan are never far from the thoughts of their loved ones.

Now, thanks to a popular family-support program, they're even closer.

Welcome to the "Flat Daddy" and "Flat Mommy" phenomenon, in which life-size cut-outs of deployed service members are given by the Maine National Guard to spouses, children, and relatives back home.

The Flat Daddies ride in cars, sit at the dinner table, visit the dentist, and even are brought to confession.
—Brian Macquarrie, “Flat-out guarding those on home front,” The Age, September 01, 2006
2003 (earliest)
Cindy Bruschwein has not seen her husband since he left for the war in Iraq.

Until he returns, there's a two-dimensional stand-in of Capt. David Bruschwein around the house — and about town. … Cindy Bruschwein, 33, enlarged a photo of her smiling, camouflage fatigue-wearing husband, and printed a life-size version of him, from the waist up .

The likeness was quickly named "Flat Dave." But to the couple's 19-month-old daughter, Sarah, the cutout is known as "Flat Daddy."
—“Flat Daddy fills in on the homefront,” Associated Press, July 19, 2003