This paper applies a physical inversion approach to retrieve geophysical properties from the single instrumental field-of-view (FOV) spectral radiances measured by the Infrared Atmospheric Sounding Interferometer (IASI) under all-sky conditions. We demonstrate the use of a principal-component-based radiative transfer model (PCRTM) and a physical inversion methodology to simultaneously retrieve cloud radiative and microphysical properties along with atmospheric thermodynamic parameters. By using a fast parameterization scheme, the PCRTM can include the cloud scattering properties simulation in radiative transfer calculations without incurring much more computational cost. The computational speed achieved for a single FOV forward simulation under cloudy skies is similar to that normally achieved for clear skies. The retrieval algorithm introduced herein adopts a novel cloud phase determination scheme, to stabilize and/or constrain retrieval iterations, based on characteristics of the reflectance and transmittance of ice and water clouds. A modified Gaussian-Newton minimization technique is employed in the iterative inversion process in order to overcome a highly nonlinear cost function introduced by the cloud parameters. We carry out a rigorous error analysis for the retrieval of temperature, moisture, ozone (O3), and carbon monoxide (CO) from IASI measurements under cloudy-sky conditions. Our algorithm is applied to real IASI observations. Retrieval results are validated using European Center for Medium-Range Weather Forecasting data and collocated Lidar/Radar measurements, and the dependence of retrieval accuracy on cloud optical depth is illustrated.