The upstream interaction of twin premixed hydrogen-air flames in 2-D turbulence is studied using direct numerical simulations with detailed chemistry. The primary objective is to determine the effect of flame stretch on the overall burning rate during various stages of the interaction. Preferential diffusion effects are accounted for by varying the equivalence ratio from symmetric rich-rich to lean-lean interactions. The results show that the local flame front response to turbulence is consistent with previous understanding of laminar premixed flames, in that rich premixed flames become intensified in regions of negative strain or curvature, while the opposite response is found for lean premixed flames. The overall burning rate history with respect to the surface density variation is found to depend on the mixture condition; the consumption rate enhancement advances (follows) the surface enhancement for the rich-rich (lean-lean) case. For the lean-lean case, a self-turbulization mechanism results in a large positive skewness in the area-weighted mean tangential strain statistics. Because of the statistical dominance of positive stretch on the flame surface, the lean-lean case results in a significantly larger burning enhancement (over a twofold increase) in addition to the surface density production. For the case of rich-rich interaction, the abundance in hydrogen species results in an instantaneous overshoot of the radical pool in the post-flame region, resulting in an additional "burst" in the reactant consumption rate history, suggesting its potential impact on the pollutant formation process.