When ultrasound is incident on a fluid-fluid interface, radiation pressure deforms the interface either along or against the incident field’s wave vector. Examples of this include: acoustic droplet ejection, acoustic fountain, and the invariant deformation of acoustically transparent interfaces. These examples consider only two fluids, and the contribution from acoustic streaming on the deformation is usually not considered. Here, we investigate the deformation of three-fluid-layer systems, one fluid layer sandwiched between two others. Here the layer thickness affects the deformation of the two interfaces due to an acoustic lensing effect and the confinement of acoustic streaming. Analytical calculations for radiation pressure and finite element method (FEM) simulations are conducted. The FEM simulations consider the deformation of the interfaces due to both radiation pressure and acoustic streaming. We report realizable configurations for these three-fluid-layer systems, namely different combinations of interface deformations either towards or away from the middle layer of the sandwich configuration and discuss possible applications of the results.