A theoretical model is reported that describes wave propagation between three floating Euler–Bernoulli thin elastic sheets extending, respectively, from $-\infty$ to 0, from 0 to $l$, and from $l$ to $\infty$, with properties, e.g. thickness, that can be specified independently. The sheets are assumed either to be welded together or to have free edges separating them. Two methods of solution are employed – the Wiener–Hopf technique and residue calculus, which allows the theoretical development to be verified at various points along the way. The model generalizes the considerable body of published work concerned with wave propagation into and out of floating ice sheets, and across features contained therein such as cracks, open or refrozen leads and embedded icebergs. It can also be applied to breakwaters, very large floating structures and vessels in a seaway. After validation, results are presented showing (a) the details of how the reflection coefficient depends on the geometry of the configuration being modelled; and (b) how a wave energy spectrum evolves as it propagates in a marginal ice zone composed of a large number of identical (coherent) or randomly specified (incoherent) sea-ice plates, as commonly observed in the polar or subpolar oceans.