A dual-container package includes a closure having a body with a first annular wall extending from the body, a second annular wall extending from the body within the first annular wall, a first dispensing opening extending through the body from between the first and second annular walls, and a second dispensing opening extending through the body from within the second annular wall. A first container is mounted to the closure by the first annular wall, and a second container is disposed within the first container and mounted to the closure by the second annular wall. The containers and the annular walls have structure for holding the containers in a predetermined angular orientation with respect to each other. In the exemplary embodiments of the disclosure, this structure includes internal beads on the annular walls received by snap fit within external channels on the neck finishes of the containers. Slots on the internal beads of the closure are received by snap fit over lugs in the container neck finish channels to prevent rotation of the containers with respect to the closure. The containers have sidewalls that can include indicia that are held in radial alignment by the closure.