End-coupling between immiscible melts of two monofunctionalized polymers of a same length was modeled by dissipative particle dynamics starting from a flat interface and up to the formation of a mature lamellar microstructure. Influence of the reaction rate, chain length, and incompatibility of components on the kinetics of copolymer formation and morphology development was investigated. Regimes of linear and logarithmic growth of the conversion with time were observed before the flat interface became unstable. The conditions and mechanism of interfacial roughness development were studied in detail. It was demonstrated that overcrowding the interface with the copolymer product causing its phase separation plays the main role in spontaneous interface distortion. The instability leads to autocatalytic interface growth with exponential kinetics, when each new portion of the product creates more area for further reactions. It was followed by a slower terminal regime including formation and ripening of the lamellar microstructure. The late stage kinetics of end-coupling was strongly influenced by depletion of reactants and formation of ordered product layers. At certain conditions, it became asymptotically diffusion controlled in agreement with published experimental data.