A composite container lid including an inner plug with a flow-out port fitted and secured to a container mouth portion and an upper lid detachably attached to the container mouth portion so as to cover the inner plug, wherein: said inner plug includes a hollow upper lid engaging cylinder with its upper end closed, a container mouth portion-securing member having a circumferential wall that surrounds said upper lid engaging cylinder, and linking pieces that link an inner surface of said circumferential wall to said upper lid engaging cylinder so as to form a flow-out port; said upper lid engaging cylinder is provided, at an upper end on an outer surface thereof, with a circumferential protuberance for temporary engagement with said upper lid; said upper lid includes a top plate and a skirt portion that stretches downward from an outer circumferential edge of said top plate and has, on the inner surface thereof, a screw thread for screw-engagement with the container mouth portion; characterized in that said top plate has engaging pieces formed on the inner surface thereof, the engaging pieces having an undercut for temporarily engaging with the circumferential protuberance that temporarily engages with said upper lid engaging cylinder; and a sound-suppressing protrusion is provided on the inner surface of said top plate in a region surrounded by said engaging pieces or on the upper end surface of said upper lid engaging cylinder, wherein a gap is maintained between the lower side surface of the screw thread of the upper lid skirt portion for screw engagement and the outer surface of the container mouth portion when said sound-suppressing protrusion starts coming in contact with the upper end surface of said upper lid engaging cylinder or with the inner surface of the top plate of said upper lid accompanying the descending motion of said upper lid. said inner plug includes a hollow upper lid engaging cylinder with its upper end closed, a container mouth portion-securing member having a circumferential wall that surrounds said upper lid engaging cylinder, and linking pieces that link an inner surface of said circumferential wall to said upper lid engaging cylinder so as to form a flow-out port; said upper lid engaging cylinder is provided, at an upper end on an outer surface thereof, with a circumferential protuberance for temporary engagement with said upper lid; said upper lid includes a top plate and a skirt portion that stretches downward from an outer circumferential edge of said top plate and has, on the inner surface thereof, a screw thread for screw-engagement with the container mouth portion; characterized in that said top plate has engaging pieces formed on the inner surface thereof, the engaging pieces having an undercut for temporarily engaging with the circumferential protuberance that temporarily engages with said upper lid engaging cylinder; and a sound-suppressing protrusion is provided on the inner surface of said top plate in a region surrounded by said engaging pieces or on the upper end surface of said upper lid engaging cylinder, wherein a gap is maintained between the lower side surface of the screw thread of the upper lid skirt portion for screw engagement and the outer surface of the container mouth portion when said sound-suppressing protrusion starts coming in contact with the upper end surface of said upper lid engaging cylinder or with the inner surface of the top plate of said upper lid accompanying the descending motion of said upper lid.