Ben Stiller has a new target to satirize: charity. Mr. Stiller, the actor known for spoofs like Zoolander and Tropic Thunder, offers a comedic take on his buddy Lance Armstrong’s Livestrong campaign on a new Web site designed to raise money for Save the Children.

In a video message to Mr. Armstrong that appears on the site, the actor lays out his “original” fund-raising idea: “Stillerstrong” headbands. Buy one, and the net proceeds go to help a school in Haiti that Mr. Stiller visited on a recent trip.

“I was thinking I could get some celebrities to wear them, like you, maybe you could wear one in your next bike race,” he says. “Let me know what you think. Tweet at me, bro. Let me [...]