Well, if your family wants to live their childhood and not relive yours, you have some affordable options.
Regal Cinemas are offering a free family film festival during the summer, which has a great price, but no locations in the immediate Denton area. More importantly, if you want to watch a family film for almost free, the Denton area offers two great options that include a chance to eat while watching the movie.
Movie Tavern in Denton sells $3 tickets to the very first show every day, Monday through Friday, and usually these are family-oriented movies. Last year, those movies included Up and Cloudy with a Chance of Meatballs, so you can expect to see quality movies. The theater also has daily food specials, such as 2-for-1 pizza on Tuesdays.
Studio Movie Grill in Lewisville will have a Summer Children's Series, on Monday through Thursday at 11 AM, with dollar tickets for children and two-dollar tickets for adults. Click the link to see a complete list of shows, which include classics such as Muppets from Space and Charlotte's Web. Studio Movie Grill also offers $2 off burgers on Tuesdays and All-You-Can-Eat Pizza on Wednesday and Thursday.
If you've never taken your family to a theater that serves food, expect somewhat inflated prices (it is a movie theater!), but nothing beats All-You-Can-Eat while watching a two-dollar movie. Plus, your kids will be so busy stuffing their faces that you won't hear a peep out of them and can actually hear Miss Piggie and Kermit's compelling dialog.
Of course, if Muppets have become compelling to you dad, then you need to get out and see a real movie like The A-Team after all. Bring more than two dollars though.