Traditional landfill cover materials have low strength and poor dry–wet durability. Municipal solid waste incineration fly ash (MSWI FA) can be used to partially replace cement solidification dredging sediment (DS). This article investigates the possibility of using MSWI FA and ordinary Portland cement (OPC) composite cured DS as a covering material. The mechanical properties, permeability, and wet–dry durability of the cured system were investigated under the conditions of MSWI FA content ranging from 0% to 60% and OPC content ranging from 10% to 15%. The microscopic mechanism was analyzed by scanning electron microscopy and X-ray diffraction. The results showed that when the OPC and MSWI FA contents were 15% and 20%, respectively, the comprehensive performance of the cured specimens was best after 28 days of natural curing. The unconfined compressive strength reached 1993.9 kPa, and the permeability coefficient decreased to below 1 × 10⁻⁷ cm/s, fully meeting the requirements for landfill coverage. C-S-H gel is the main strength source of the solidified body, while Friedel salt and ettringite enhance the compactness of the matrix. An excessive moisture environment promotes the water absorption of soluble salts produced by MSWI FA hydration, leading to sample expansion and reduced strength. MSWI FA and OPC cured DS exhibit good compression performance in the intermediate cover system of landfills, and can maintain good engineering performance under periodic dry–wet cycles. This dual strategic synergy solves the hazardous disposal problem of MSWI FA and the resource utilization demand of DS, demonstrating enormous application potential.