In vision-and-language grounding problems, fine-grained representations of the image are considered to be of paramount importance. Most of the current systems incorporate visual features and textual concepts as a sketch of an image. However, plainly inferred representations are usually undesirable in that they are composed of separate components, the relations of which are elusive. In this work, we aim at representing an image with a set of integrated visual regions and corresponding textual concepts, reflecting certain semantics. To this end, we build the Mutual Iterative Attention (MIA) module, which integrates correlated visual features and textual concepts, respectively, by aligning the two modalities. We evaluate the proposed approach on two representative vision-and-language grounding tasks, i.e., image captioning and visual question answering. In both tasks, the semantic-grounded image representations consistently boost the performance of the baseline models under all metrics across the board. The results demonstrate that our approach is effective and generalizes well to a wide range of models for image-related applications. (The code is available at \url{https://github.com/fenglinliu98/MIA)