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A critical challenge in biomechanical simulations is the spatial discretization of complex fluid-solid geometries created from imaging. This is especially important when dealing with Lagrangian interfaces, as there must be at a minimum both geometric and topological compatibility between fluid and solid phases, with exact matching of the interfacial nodes being highly desirable. We have developed a solution to this problem and applied the approach to the creation of a 3D fluid-solid mesh of the mouse heart. First, a 50 micron isotropic MRI dataset of a perfusion-fixed mouse heart was segmented into blood, tissue, and background using a customized multimaterial connected fuzzy thresholding algorithm. Then, a multimaterial marching cubes algorithm was applied to produce two compatible isosurfaces, one for the blood-tissue boundary and one for the tissue-background boundary. A multimaterial smoothing algorithm that rigorously conserves volume for each phase simultaneously smoothed the isosurfaces. Next we applied novel automated meshing algorithms to generate anisotropic hybrid meshes with the number of layers and the desired element anisotropy for each material as the only input parameters. As the meshes are scale-invariant within a material and include boundary layer prisms, fluid-structure interaction computations would have a relative error equilibrated over the entire mesh. The resulting model is highly detailed mesh representation of the mouse heart, including features such as chordae and coronary vasculature, that is also maximally efficient to produce the best simulation results for the computational resources available.