Precocious Alex

I'm reading Julia Child's My Life In France, which she wrote with Alex Prud'Homme. In the introduction is this sentence, which isn't exactly a garden path but did baffle me mightily till I was halfway through it:

Alex was born in 1961, the year that our first book, Mastering the Art of French Cooking, which I wrote with Simone Beck and Louisette Bertholle, was published.

The problem is that "our", of course; I wanted it to mean "Alex and I", which is pragmatically impossible. Its actual antecedent comes after it (how wacky is it we still call it the antecedent? But why multiply names without reason, as Occam almost said), and once you hit it, the sentence is clear. I think I'd have written "my book" - maybe I'm not as modest as Julia. Or even just dropped the possessive determiner entirely and said "the first book I wrote with ..."