Is the marriage of disbelievers valid? Were the parents of Prophet (PBUH) married as per Islamic law?

A Christian brought this argument. He stated that under Islam the polytheist marriage isn't exactly "valid". He stated the fact that the Prophet was born out of a disbeliever makes him a child of adultery (audhubillah). This really disturbed me and I wanted to make sure what the take is. I've already read ahadith where the Prophet stated that he wasn't allowed to supplicate for his mother indicating she died upon disbelief.