There seem to be some errors here:
- There is no monthly pass for the Half-Fare Card, only an annual pass.
- Children travel free only up to and including the age of 5. After that they need their own ticket (up to and including the age of 15 they pay only half), no matter if the parents have a Half-Fare Card or other subscription or not.
For accompanied children there are the following savings offers:
Single days with the https://www.sbb.ch/en/travelcards-and-tickets/tickets-for-switzerland/day-pass/day-pass-children.html
A whole year with the https://www.sbb.ch/en/travelcards-and-tickets/railpasses/junior-travelcard.html
However, you can also save money if you buy the individual tickets as a saver ticket, as long as the trip is far enough in the future and you can already commit to a certain train.