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Air cushioning of a high-speed liquid droplet impact with a finite-depth liquid layer sitting upon a rigid impermeable base is investigated. The evolution of the droplet and liquid-layer free-surfaces is studied alongside the pressure in the gas film dividing the two. The model predicts gas bubbles are trapped between the liquid free-surfaces as the droplet approaches impact. The key balance in the model occurs when the depth of the liquid layer equals the horizontal extent of interactions between the droplet and the gas film. For liquid layer depths significantly less than this a shallow liquid limit is investigated, which ultimately tends towards the air-cushioning behavior seen in droplet impact with a solid surface. Conversely, for liquid layer depths much deeper than this, the rigid base does not affect the air-cushioning of the droplet. The influence of compressibility is discussed and the relevant parameter regime for an incompressible model is identified. The size of the trapped gas bubble as a function of the liquid layer depth is investigated. The deep water model is extended to consider binary droplet collisions. Again, the model predicts gas bubbles will be trapped as the result of air cushioning in high-speed binary droplet impacts. [ABSTRACT FROM AUTHOR]