I was covered under my parents passport when I was younger (take it this is what people are referring to as a 'child's passport'). When I applied for my first adult passport I had to go for an interview...This was about 5-6 years ago.
Children used to be put under a parents passport but that changed ages ago.
Our 2 year old has his own passport independent from us. Not that he can go anywhere without us as he has no money and mooches off us.