It is not normal, and it is a straightforward diagnosis: there is too much water inside your car.
Interior frost is condensation that froze. Warm air holds moisture; when the car cools overnight the moisture comes out onto the coldest surface, which is the glass, and below freezing it forms frost rather than mist.
A car with a normal amount of moisture in it gets a little mist. A car with a wet interior gets what you are describing, which is why your neighbours do not have it. And the fact that it is worse after rain is the clearest possible clue.
So find the water. In order of likelihood:
Wet carpets and mats. Feel them, and lift the mats and feel underneath. A soaked underlay holds litres and releases it slowly for weeks.
A leak. Blocked drainage channels around the windscreen and sunroof are the classic, and they push water into the footwells. Door and boot seals next.
Wet things left in the car - coats, umbrellas, gym kit, a dog.
A leaking heater matrix, which usually smells sweet and leaves an oily film on the inside of the glass.
Dry the interior properly and the problem largely disappears.