While detailed theories exist for thermal conduction due to electrons and phonons in crystalline solids, phonon scattering and transmission at solid/solid interfaces is not as well understood. Steady increases in the power density of microelectronic devices have resulted in an increasing need in the electronics industry for an understanding of thermal conduction in multilayered structures. The materials of interest in this study consist of a polymer matrix in which small (on the order of microns to tens of microns) highly conductive filler particles (such as Ag or alumina) are suspended. These materials are used to form a thermal interface material bondline (a fifty to several hundred micron bonding layer) between a power device and a heat spreader. Such a bondline contains many polymer/filler interfaces. Using a micro Fourier apparatus, the thermal conductivities of such thermal interface material (TIM) bondlines of various thicknesses, ranging from fifty microns to several hundred microns, have been measured. The microstructure of these bondlines has been investigated using optical microscopy and acoustic microscopy. Measured values of thermal conductivity are compared to values for bulk samples, and considered in terms of microstructural features such as filler particle depleted regions. The influence of polymer/filler particle interfaces in the TIM bondline on phonon transport through the bondline is also considered.