In the TNG3x14: "A Matter of Perspective", the ship's interior panels are stated by Geordi to be made of "solid duranium". The ship's bulkheads (structural walls) are composed of Tritanium (TNG2x02 "Where Silence Has Lease). As for interior amenities like paneling the ship has wood (Worf's station), transparent aluminum (skylight/skydome and windows) Also probably made of the same metals for use then laminated with wood, plastic or soft touch/tone materials for aesthetic. Just as real naval ships are built with all steel construction.
Whatever interior fillings they use for the ship we know they have metal doors. We know they have carpet and rugs. Given the 24th century aversion to "Utilizing animals for food/products" leather is presumably synthetic. Tables are made of glass, metal, Lucite, and polycarbonate. A lot of the furniture was made of synthetic fabric and plastics and aluminum. The companies Artifort and HAG made chairs/seating that was utilized by the Paramount studios for the seating in the series. A lot of the set was plastic, resin, or plywood painted to resemble metal. Polyester (a real plastic) was a material used by Starfleet in the 23rd century - bedsheets and blankets were made of this material. "Steelplast" was a thin material used in the construction of walls.
Study NASA's use of material science for spacecraft, to prevent fire they bought or developed various materials to protect astronauts from the hazards of potential spark, fire and toxicity. They made fabrics with materials like Chromel-R (woven steel) and beta cloth (fiber glass woven like a blanket and coated in Teflon) to produce materials aboard space craft that wouldn't burn.