Porous materials such as sandstones have important applications in petroleum engineering and geosciences. An accurate knowledge of the porous microstructure of such materials is crucial for the understanding of their physical properties and performance. Here, we present a procedure for accurate reconstruction of porous materials by stochastically fusing limited bimodal microstructural data including limited-angle X-ray tomographic radiographs and 2D optical micrographs. The key microstructural information contained in the micrographs is statistically extracted and represented using certain lower-order spatial correlation functions associated with the pore phase, and a probabilistic interpretation of the attenuated intensity in the tomographic radiographs is developed. A stochastic procedure based on simulated annealing that generalizes the widely used Yeong-Torquato framework is devised to efficiently incorporate and fuse the complementary bimodal imaging data for accurate microstructure reconstruction. The information content of the complementary microstructural data is systematically investigated using a 2D model system. Our procedure is subsequently applied to accurately reconstruct a variety of 3D sandstone microstructures with a wide range of porosities from limited X-ray tomographic radiographs and 2D optical micrographs. The accuracy of the reconstructions is quantitatively ascertained by directly comparing the original and reconstructed microstructures and their corresponding clustering statistics.