Maris - he sounds terminally confused to me! It is tough when OW calls on the house phone: making a fuss looks like we are givng them too much head-room.
My line was to say politely that it was unacceptable. Cell phones are designed for affairs, and to keep them out of the family domain, and that in future you would prefer it if she didn't phone your home. This isn't about him, it is about boundaries of acceptable behaviour. My h got blustery about it, but I said that the pohone bill was a family expense, and that I would not take calls from someone he disapproved of. He sulked, but basically accepted what I said.