Polymer-modified materials provide numerable enhancements to cementitious composites. However, the curing/hardening conditions for cementitious and polymeric materials differ significantly, although they are mixed to form a single entity. Cement requires a moist environment for the hydration process to occur, while polymers require a hot and dry environment. Consequently, the polymer-modified composite exhibits lower compressive strength than the ordinary cementitious product. The objective of the present study was to resolve this issue by using accelerated curing regimens, following the fundamental concept that the dominant contribution to the toughness of the composite matrix is from the cement system, while polymer films refine the microstructure. Hygrothermal treatment for plain mortar was first developed in order to achieve 100% of the 28-day strength after treatment is completed. The hot + dry treatment required for the formation of polymer film was studied in the second phase of this study, together with an investigation of the microstructure using scanning electron microscopy. The results show that, after being subjected to the hygrothermal and hot + dry treatment, polymer-modified mortar can achieve low intrinsic permeability without compromising the compressive strength. A 15% polymer loading in styrene–butadiene rubber- and epoxy-modified mortar led to 46% and 18% higher compressive strengths, and 660% and 460% lower intrinsic permeabilities, compared with unmodified mortar, respectively.