In this research, optimization of the integrated biodiesel production process composed of transesterification of edible sunflower oil, catalyzed by commercial lipase, with simultaneous extraction of glycerol from the reaction mixture was performed. Deep eutectic solvents (DESs) were used in this integrated process as the reaction and extraction media. For two systems, choline chloride:glycerol (ChCl:Gly) and choline chloride:ethylene glycol (ChCl:EG), respectively, the optimal water content, mass ratio of the phase containing the mixture of reactants (oil and methanol) with an enzyme and a DES phase (mass ratio of phases), and the molar ratio of deep eutectic solvent constituents were determined using response surface methodology (RSM). Experiments performed with ChCl:Gly resulted in a higher biodiesel yield and higher glycerol extraction efficiency, namely, a mass ratio of phases of 1:1, a mass fraction of water of 6.6%, and a molar ratio of the ChCl:Gly of 1:3.5 were determined to be the optimal process conditions. When the reaction was performed in a batch reactor under the optimal conditions, the process resulted in a 43.54 ± 0.2% yield and 99.54 ± 0.19% glycerol extraction efficiency (t = 2 h). Unfortunately, the free glycerol content was higher than the one defined by international standards (wG > 0.02%); therefore, the process was performed in a microsystem to enhance the mass transfer. Gaining the same yield and free glycerol content below the standards (wG = 0.0019 ± 0.003%), the microsystem proved to be a good direction for future process optimization.