Abstract. Mixed-phase clouds are not well represented in climate and weather forecasting models, due to a lack of the key processes controlling their life cycle. Developing methods to study these clouds is therefore essential, despite the complexity of mixed-phase cloud processes and the difficulty of observing two cloud phases simultaneously. We propose in this paper a new method to retrieve the microphysical properties of mixed-phase clouds, ice clouds and supercooled water clouds using airborne or satellite radar and lidar measurements, called VarPy-mix. This new approach extends an existing variational method developed for ice cloud retrieval using lidar, radar and passive radiometers. We assume that the lidar attenuated backscatter β at 532 nm is more sensitive to particle concentration and is consequently mainly sensitive to the presence of supercooled water. In addition, radar reflectivity Z at 95 GHz is sensitive to the size of hydrometeors and hence more sensitive to the presence of ice particles. Consequently, in the mixed phase the supercooled droplets are retrieved with the lidar signal and the ice particles with the radar signal, meaning that the retrievals rely strongly on a priori and error values. This method retrieves simultaneously the visible extinction for ice αice and liquid αliq particles, the ice and liquid water contents IWC and LWC, the effective radius of ice re,ice and liquid re,liq particles, and the ice and liquid number concentrations Nice and Nliq. Moreover, total extinction αtot, total water content (TWC) and total number concentration Ntot can also be estimated. As the retrieval of ice and liquid is different, it is necessary to correctly identify each phase of the cloud. To this end, a cloud-phase classification is used as input to the algorithm and has been adapted for mixed-phase retrieval. The data used in this study are from DARDAR-MASK v2.23 products, based on the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) and Cloud Profiling Radar (CPR) observations from the CALIPSO and CloudSat satellites, respectively, belonging to the A-Train constellation launched in 2006. Airborne in situ measurements performed on 7 April 2007 during the Arctic Study of Tropospheric Aerosol, Clouds and Radiation (ASTAR) campaign and collected under the track of CloudSat–CALIPSO are compared with the retrievals of the new algorithm to validate its performance. Visible extinctions, water contents, effective radii and number concentrations derived from in situ measurements and the retrievals showed similar trends and are globally in good agreement. The mean percent error between the retrievals and in situ measurements is 39 % for αliq, 398 % for αice, 49 % for LWC and 75 % for IWC. It is also important to note that temporal and spatial collocations are not perfect, with a maximum spatial shift of 1.68 km and a maximum temporal shift of about 10 min between the two platforms. In addition, the sensitivity of remote sensing and that of in situ measurements is not the same, and in situ measurement uncertainties are between 25 % and 60 %.