In this paper, we analyse sea ice freezing in the presence of a two-phase (mushy) layer filled with ice structures and salt water. An exact analytical solution of moving boundary problem is constructed with allowance for turbulent motion of sea water at the phase interface between the mushy layer and ocean. As a result, the temperature and salinity distributions as well as the sea ice fraction are found analytically. The laws of motion for the phase transition boundaries “sea ice–mushy layer” and “mushy layer–ocean” are derived as well. In addition, such structural characteristics of sea ice as its permeability and primary interdendritic spacing are calculated. The heat fluxes (thermal flux emanating from ice surface, thermal flux caused by ice freezing in a mush and residual heat flux caused by ocean cooling) governing the heat budget and influencing climate dynamics and circular air currents over a freezing ocean are analytically deduced too. We analyse how sea ice freezes in the presence of a mushy layer when fluctuations in the atmospheric temperature and friction velocity occur. For this purpose, we introduce corresponding fluctuations based on the Langevin equation and Ornstein–Uhlenbeck stochastic processes. Two types of noises, additive and multiplicative, are considered. The analytical solution obtained is then analysed with allowance for stochastic fluctuations in the atmospheric temperature and friction velocity. One of the main results is that the permeability of sea ice and average interdendritic spacing of ice crystals in the two-phase layer increase as the noise intensity increases. Another important conclusion is that the mushy layer, representing the layer of ice and salt water, becomes thicker and the ocean freezes faster when fluctuations in the atmospheric temperature and friction velocity occur. © 2023, The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature.