Clearly your issue is with language and law.
Interfaith marriage is illegal by state law in Israel. They won’t recognise it.
Interfaith marriage is recognised in the Lebanon. This means it is up to the place, body or representative of worship to decide. Example: as far as I’m aware Catholics will only marry Catholics in church. Whereas most Protestant churches don’t care, they’re just happy to take the money and maybe get a new adherent.
So illegal by state law in Israel. Legal in the Lebanon.
Not rocket science! Try reading more slowly!!!