I Found You by Lisa Jewell

Alice observes a man on the beach. He sits for hours, even in the rain. She brings him a jacket. He doesn't know who he is. She asks him to her chaotic home, with two teenagers a grade school daughter, and three dogs. Meanwhile in London, Lily's husband hasn't returned from work, she just knows something is wrong. Now we become involved in the lives of Alice and Lily. The story alternates between the two characters until about three quarters of the way through, when their paths cross and the answers slowly come to light. A double fold missing person mystery all the way around!