Robotic manipulation, in particular in-hand object manipulation, often requires an accurate estimate of the object’s 6D pose. To improve the accuracy of the estimated pose, state-of-the-art approaches in 6D object pose estimation use observational data from one or more modalities, e.g., RGB images, depth, and tactile readings. However, existing approaches make limited use of the underlying geometric structure of the object captured by these modalities, thereby, increasing their reliance on visual features. This results in poor performance when presented with objects that lack such visual features or when visual features are simply occluded. Furthermore, current approaches do not take advantage of the proprioceptive information embedded in the position of the fingers. To address these limitations, in this paper: (1) we introduce a hierarchical graph neural network architecture for combining multimodal (vision and touch) data that allows for a geometrically informed 6D object pose estimation, (2) we introduce a hierarchical message passing operation that flows the information within and across modalities to learn a graph-based object representation, and (3) we introduce a method that accounts for the proprioceptive information for in-hand object representation. We evaluate our model on a diverse subset of objects from the YCB Object and Model Set, and show that our method substantially outperforms existing state-of-the-art work in accuracy and robustness to occlusion. We also deploy our proposed framework on a real robot and qualitatively demonstrate successful transfer to real settings