The treehouse is only truly explorable during the intermissions between cases. You'll get access to this early on and are introduced to the tickertype for your missions. The goal is to visit every area in and around the house before you use the tickertype. You'll start in what I'll claim is the third floor, the living room. The treehouse is divided into several floors.
First Floor: Treasury (connected to: Outside, Kitchen
Second Floor: Kitchen (connected to: Bathroom, Armory, Living Room
Third Floor: Living Room, where you start (connected to: Playroom, Bedroom
, Crow's Nest
You can visit some of these in one intermission and finish the rest on another intermission, so don't be afraid if you don't get this before entering the first case.