What is the meaning of "facade"?

Jeff plays along, his tough-guy tone pitched somewhere between Robert Mitchum and Dana Andrews. “Put Miss Carpenter on the horn. I need to talk to her pronto.”
“Miss Carpenter is busy with an important case. May I take a message?”
“Yeah,” Jeff says. “Tell her my flight from Chi-Town has been delayed.”
My façade drops. “Oh, Jeff. Really?”
“Sorry, hon. The perils of flying out of the Windy City.”
“How long is the delay?”
“Anywhere from two hours to maybe-I’ll-be-home-by-next-week,” Jeff says. “I’m at least hoping it’s long enough for me to miss the start of Baking Season