If, like me, you have an ‘Italian’ child, ie a child that was born in Italy, then it is possible that this child is included on the mother’s passport, assuming that the child is under 18.
What happens though, if the father wants to take the child out of Italy, without the mother?
Well, there is a solution. You can apply for a children’s ID card, and this can then be used to travel within those European countries which have signed the Schengen Agreement. Italian ID cards are also accepted as travel documents in some other countries, such as Egypt for example.

Stop reading, start speaking
Stop translating in your head and start speaking Italian for real with the only audio course that prompt you to speak.
I’ve managed to track down details of the application procedure on the Vice Consulate of Italy, Bedford site. You will need to scroll down to the Italian ID Card section at the end of the page for more information and all the forms you will need.
I do know of a couple who did not bother putting their young one on the mother’s passport, but instead just applied for a children’s ID card. What I do not know is for how long these ID cards are valid.
One other thing you may like to note is that non-Italian citizens, like me, who have an Italian ID card, cannot use their version of the ID card to travel outside of Italy. We still need our passports.
I also believe that the UK and Ireland are not part of the Schengen Agreement, so a full passport is needed to enter these countries.