Two children discover that they are having the same recurring nightmare, featuring a small boy in danger, although each notice details the other doesn’t; trying to track the source of the dream puts them in the way of a shadowy and evil government agency, who are trying to cover up a possible alien incursion.

I believe I encountered House of Stairs first, but Into the Dream is the one I remembered for years without retaining either the title or the author: which meant all I remembered were details of the dream ("Jaleela . . . Jaleela"), which in appropriately meta fashion I eventually used to track the book down.