The interaction between sea ice and atmosphere depends strongly on the near-surface transfer coefficients for momentum and heat. A parametrization of these coefficients is developed on the basis of an existing parametrization of drag coefficients for neutral stratification that accounts for form drag caused by the edges of ice floes and melt ponds. This scheme is extended to better account for the dependence of surface wind on limiting cases of high and low ice concentration and to include near-surface stability effects over open water and ice on form drag. The stability correction is formulated on the basis of stability functions from Monin-Obukhov similarity theory and also using the Louis concept with stability functions depending on the bulk Richardson numbers. Furthermore, a parametrization is proposed that includes the effect of edge-related turbulence also on heat transfer coefficients. The parametrizations are available in different levels of complexity. The lowest level only needs sea ice concentration and surface temperature as input, while the more complex level needs additional sea ice characteristics. An important property of our parametrization is that form drag caused by ice edges depends on the stability over both ice and water which is in contrast to the skin drag over ice. Results of the parametrization show that stability has a large impact on form drag and, thereby, determines the value of sea ice concentration for which the transfer coefficients reach their maxima. Depending on the stratification, these maxima can occur anywhere between ice concentrations of 20 and 80%.