Using dissipative particle dynamics simulation, we probe the tunable permeability of cross-linked microcapsules made from pH-sensitive diblock copolymers poly(ethylene oxide)-b-poly(N,N-diethylamino-2-ethyl methacrylate) (PEO-b-PDEAEMA). We first examine the self-assembly of non-cross-linked microcapsules and their pH-responsive collapse and then explore the effects of cross-linking and block interaction on the swelling or deswelling of cross-linked microcapsules. Our results reveal a preferential loading of hydrophobic dicyclopentadiene (DCPD) molecules in PEO-b-PDEAEMA copolymers. Upon reduction of pH, non-cross-linked microcapsules fully decompose into small wormlike clusters as a result of large self-repulsions of protonated copolymers. With increasing degree of cross-linking, the morphology of the microcapsule becomes more stable to pH change. The highly cross-linked microcapsule shell undergoes significant local polymer rearrangement in acidic solution, which eliminates the amphiphilicility and therefore enlarges the permeability of the shell. The responsive cross-linked shell experiences a disperse-to-buckle configurational transition upon reduction of pH, which is effective for the steady or pulsatile regulation of shell permeability. The swelling rate of the cross-linked shell is dependent on both electrostatic and nonelectrostatic interactions between the pH-sensitive groups as well as the other groups. Our study highlights the combination of cross-linking structure and block interactions in stabilizing microcapsules and tuning their selective permeability.