Prince William and Kate's baby due in July, palace officials say Britain's Prince William leaves the King Edward VII hospital with his wife Catherine, Duchess of Cambridge, London December 6, 2012. Prince William's pregnant wife Kate left the King Edward VII hospital in central London on Thursday where she had spent four days being treated for acute morning sickness. Palace officials say Prince William and the former Kate Middleton's first baby is due in July and that her condition is improving. The Duchess of Cambridge, as she is formally known, had been hospitalized earlier in her pregnancy for acute morning sickness. Officials said Monday she is feeling better. She made a rare public appearance last week and appeared to be healthy. The infant would be third in line for the British throne.