The vertical stabilizer of Boeing's 777 is composite.
--Boot Hill
The skins AND the spars? Or only the skins? Big difference, obviously. I don't know if the Airbus spars are composite or not - perhaps none of them are? The spars are primary structure, as are the attach flanges.
You said something about a chunk of titanium in place of the composite in an earlier post. Titanium weighs quite a bit more than aluminum and composite for equivalent loads and temperatures. Titanium is used when you need a high-emperature capability (but not as high as steel) but want to save weight over steel. Aluminum is only 10-15% heavier than carbon-fiber composites for equal loads and temperatures. However, aluminum yields plastically and fails gradually while composites yield quickly and fail quickly - so aluminum as a much better choice for low temperature primary structure.