What is the correct way to write multiple possessives, rather than the common way?

In the phrase, "Tim Rice and Andrew Lloyd Webber's Jesus Christ Superstar...," I believe Rice should end in 's, as Webber does, because the show is as much Rice's as it is his partner's. However, whenever I've seen multiple nouns in a possessive, the first noun does not have thhe 's. I cannot fine a grammar rule to address this. Is it a case in which people have written and said it wrong for so long, the incorrect use has become acceptable? Which use is correct?