We present a finite-element software library, IRENE, for numerically solving the steady state and dynamics of a two-dimensional viscous fluid layer embedded in three-dimensional space, on multiple physical scales. The library is designed to handle a wide range of physical regimes – both low-Reynolds-number and turbulent ones – and geometries, capturing the coupling between in-plane flows, out-of-plane deformations, surface tension, and elastic response. In addition, the software can treat complex geometries, including those with intra-layer obstacles or arbitrary layer boundaries. We validate IRENE against known analytical and numerical results and demonstrate its capabilities through examples relevant to biological membranes and macroscopic air flows.