Sarah and Richard Newman are Sophie and Josh's parents. Or at least we think they are. To be honest, they're totally M.I.A. for the entire book. Mr. and Mrs. Newman dump the twins with their Aunt Agnes in San Francisco over the summer while they are on loan to the University of San Francisco as archaeologists.
We get the sense that Sophie and Josh's parents care about them, but that they don't really take the time to get to know them: "Josh always said that their parents lived five million years in the past and were only happy when they were up to their ankles in mud. The twins knew that they were loved unconditionally, but they also knew that their parents simply didn't understand them... or much else about modern life" (8.25).
The twins constantly say that they've come to rely on each other so much because their parents are away so much of the time, and the sentiment is reflected in the book itself; their parents don't make a single appearance. Check out the themes of "Family" and "Youth" for more about how the twins seem to be more responsible than their own 'rents.