willis1217009_01_X17230crop.jpgBruce Willis and his wife Emma Heming are expecting their first baby together, rep confirms.

A source close to the couple tells Life & Style, "Emma is showing!"

Willis, 56, and Heming, 33, got married back in 2009.

The Die Hard actor already has three daughters with ex wife Demi Moore ... Rumer, 23, Scout, 20 and Tallulah, 17.

The source adds, "Emma is living Demi’s dream."