"I thought we were invited to your parents' house for dinner."
Because I'm so critical about food, people don't want to invite me home for dinner.
Maybe one of them had invited him home for lunch or dinner.
They then met the rest of the household and were invited for dinner.
But one night he invited me to his home for dinner.
What you should do is invite her round for dinner.
They would invite you for dinner; so it was special.
When he'd called and said he wanted to see her, she'd invited him for dinner.
He invited me to his house for dinner, and we became great friends.
The next evening, we were invited for dinner at her home.