A ceiling system including: a ceiling structure suspended in an interior space. The ceiling structure includes: a perimeter frame defining a central opening, the perimeter frame comprising a fabric gripping member; a support grid comprising a plurality of intersecting struts defining a plurality of grid openings, the support grid disposed within the central opening and coupled to the perimeter frame; a plurality of acoustic ceiling panels, each of the acoustic ceiling panels mounted to the support grid and disposed in one of the grid openings; and a tensioned fabric sheet having a perimeter portion that is engaged by the fabric gripping member of the perimeter frame, the tensioned fabric sheet located below the acoustic ceiling panels and covering the central opening.