A storage bin assembly has a container base with a front, a back, a bottom, a perimeter side wall extending up from the bottom, and a storage space above the bottom within the side wall. A base lid is positioned over a top of the storage space. An access opening into the storage space is positioned near the front of the container base. A cover is selectively movable relative to the lid between a closed position closing off the access opening and two optional open positions. One of the positions is a rear position rearward of the access opening and the other of the positions is a front position forward of the access opening. Each optional open position exposes the storage space through the access opening.