We present a novel approach to the retrieval of aerosol properties from multiple-wavelength single-viewing-angle measurements of intensity as well as polarization. Instead of assuming a number of standard aerosol models, the presented method aims to retrieve microphysical aerosol properties corresponding to a bimodal aerosol size distribution. Additionally, the oceanic pigment concentration and information on aerosol height are retrieved from the measurement. The retrieval approach is based on a linearized vector radiative transfer model in combination with the Phillips-Tikhonov regularization method. Aerosol retrievals are performed on synthetic GOME-2 measurements of intensity and polarization. Here, the information content of retrievals using intensity as well as polarization measurements is investigated and compared with retrievals using only intensity measurements. It is found that for retrievals that include polarization measurements the degrees of freedom for signal (DFS) is in the range 6--8. Here, the aerosol loading of both modes, the effective radius of at least one mode, the real and imaginary part of the refractive index, the height of the layer where the bulk of the aerosols is located, and the oceanic pigment concentration can be retrieved from the measurement. For some aerosol types also, information on the effective variance can be retrieved. If only intensity measurements are used, the DFS is in the range 3.5--5 and no significant information on aerosol imaginary refractive index, effective variance, and aerosol height can be retrieved. For most viewing geometries, the expected uncertainty on the aerosol optical thickness at 550 nm is in the range 3--5% if intensity and polarization measurements are used and is a factor 2--30 higher if only intensity measurements are used. The absolute uncertainty on the single scattering albedo at 350 nm is about 0.015 for retrievals including polarization and 0.025--0.2 for retrievals using only intensity measurements. Additionally, the effect of systematic errors has been investigated. The effect of a 1% calibration error is below 10% on the optical thickness at 550 nm but can be as large as 0.06 (absolute error) on the single scattering albedo, depending on the spectral signature and aerosol type.