Keywords: Statistical Mechanics, Soft Condensed Materials, Stochastic Eulerian Lagrangian Methods, Fluid Dynamics. Abstract: A modeling and simulation formalism is presented for the study of soft materials. The formalism takes into account microstructure elasticity, hydrodynamic interactions, and thermal fluctuations. As a specific motivation we consider lipid bilayer membranes and polymeric fluids. The approach couples a Lagrangian description of the microstructures (lipid molecules / polymers) with an Eulerian description of the hydrodynamics. Thermal fluctuations are incorporated in the formalism by an appropriate stochastic forcing of the resulting equations in accordance with the principles of statistical mechanics. The overall approach extends previous work on the Stochastic Immersed Boundary Method. Simulation studies are presenting showing applications of the methodology in the study of lipid flow in bilayer membranes, the shear viscosity of polymer fluids and lipid structures, and the diffusivity of particles in complex fluids.