A facile way to generate compatibilized blends of immiscible polymers is through reactive blending of end-functionalized homopolymers. The reaction may be reversible or irreversible depending on the end-groups and is affected by the immiscibility and transport of the reactant homopolymers and the compatibilizing copolymer product. Here we describe a phase-field framework to model the combined dynamics of reaction kinetics, diffusion, and multi-component thermodynamics on the evolution of the microstructure and reaction rate in reactive blending. A density functional with no fitting parameters, which is obtained by adapting a framework of Uneyama and Doi and qualitatively agrees with self-consistent field theory, is used in a diffusive dynamics model. For a symmetric mixture of equal-length reactive polymers mixed in equal proportions, we find that depending on the Flory χ parameter, the microstructure of an irreversibly reacting blend progresses through a rich evolution of morphologies, including from two-phase coexistence to a homogeneous mixture, or a two-phase to three-phase coexistence transitioning to a homogeneous blend or a lamellar copolymer. The emergence of a three-phase region at high χ leads to a previously unreported reaction rate scaling. For a reversible reaction, we find that the equilibrium composition is a function of both the equilibrium constant for the reaction and the χ parameter. We demonstrate that phase-field models are an effective way to understand the complex interplay of thermodynamic and kinetic effects in a reacting polymer blend.