In this paper, a coupled inverse analysis is proposed to identify nonlinear compressible hyperelastic material models described by two sets of experiments. While the overall approach is applicable for different materials, here it will be presented for viable lung parenchyma. Characterizing the material properties of lung parenchyma is essential to describe and predict the mechanical behavior of the respiratory system in health and disease. During breathing and mechanical ventilation, lung parenchyma is mainly subjected to volumetric deformations along with isochoric and asymmetric deformations that occur especially in diseased heterogeneous lungs. Notwithstanding, most studies examine lung tissue in predominantly isochoric tension tests. In this paper, we investigate the volumetric material behavior as well as the isochoric deformations in two sets of experiments: namely, volume-pressure-change experiments (performed with 287 samples of 26 rats) and uniaxial tension tests (performed with 30 samples of 5 rats). Based on these sets of experiments, we propose a coupled inverse analysis, which simultaneously incorporates both measurement sets to optimize the material parameters. Accordingly, we determine a suitable material model using the experimental results of both sets of experiments in one coupled identification process. The identified strain energy function with the corresponding material parameters [Formula: see text] is validated to model both sets of experiments precisely. Hence, this constitutive model describes the complex volumetric and isochoric nonlinear material behavior of lung parenchyma. This derived material model can be used for nonlinear finite element simulations of lung parenchyma and will help to quantify the stresses and strains of lung tissue during spontaneous and artificial breathing; thus, allowing new insights into lung function and biology.