Trim crust from bread; discard. Cut bread into 2-inch cubes; place in a large bowl.
Melt butter and cheeses in a saucepan over low heat; stir occasionally.
Beat whites at high speed with an electric mixer until stiff peaks form; fold one-quarter of whites into cheese mixture. Fold into remaining whites. Pour over bread cubes, tossing to coat. Place bread cubes in a single layer on an ungreased cookie sheet.