“This is a family show” is a frequent radio or television program admonition to keep it clean—no obscenities are allowed. The “family show” saying is often given with some irony. For example, the host of a late night program might caution a guest that he’s hosting a “family show,” even though young family members are not expected to be awake and watching or listening at that late hour.  Also, television “family shows” such as The Jerry Springer Show and The Maury Povich Show feature dysfunctional families and are usually too strong for younger family viewers.
 
“This is a family show,” joked Dean Martin (1917-1995) about his comedy-variety series The Dean Martin Show in 1965. “Mom, Dad and the kids can sit around the bar and watch it.”
 
Newspapers have long printed a similar saying in “This is a family newspaper” (cited in print since at least 1881).
 
 
17 September 1965, Oakland (CA) Tribune, “On Television” by Bob MacKenzie, pg. 24, col. 1:
“This is a family show.” oozed Dean Martin. “Mom, Dad and the kids can sit around the bar and watch it.”
     
22 March 1969, Wichita (KS) Eagle and Beacon, “Life Is a Circus to Ladies of the Big Top” by Sharon McEachern, pg. 4A, col. 4:
The response was groans and a few curse words.
 
“Ah-ah, don’t talk like that—this is a family show,” cautioned petite, 18-year-old Donna Lockard.
 
12 May 1976, State-Times (Baton Rouge, LA), “Channel Chuckles” by Bill Keane, pg. 17-D, col. 1:
“It’s okay. Mommy—this is a family show.”
(The young boy is watching a television show titled “THE MANSON FAMILY”—ed.)
 
Google Books
March 1985, Cincinnati magazine, pg. 93, col. 2:
TOM: Well, there’s a joke going around town that when Smilin’ Bill heard his company had to have relations with the public, he thought they meant he was supposed to —
NORM: Hold on, there, Tom. This is a family show.
 
Google Books
Class Acts:
Plays & Skits for Jewish Settings
By Stan J. Beiner
Denver, CO: A.R.E. Pub.
1992
Pg. 79:
So, go ahead with your comments, but remember, this is a family show.
 
Google Books
Antiques Roadshow Behind the Scenes:
An Insider’s Guide to PBS’s #1 Weekly Show
By Marsha Bemko
New York, NY: Touchstone (Simon & Schuster)
2009
Pg. 76:
“There’s even the occasional ‘nasty’ word sprinkled in, but sometimes we just bleep those, because they can be entertaining. We do tend to err on the side of politeness and good taste. After all, this is a family show.”
 
Google Books
The Clique #12:
These Boots Are Made for Stalking
By Lisi Harrison
New York, NY: Little, Brown and Company
2010
Pg. ?:
“Dude, this is a family show. Keep it clean.”