Coupling structures of buoyancy induced thermal convection in two immiscible layers with and without weak background rotation were investigated in laboratory experiments using a glycerol solution and a silicon oil as the test fluids. A cylindrical vessel was employed to yield three-dimensional (3D) development of the two-layer convection, and the influence of background rotation on convective motion was investigated to imitate the rotation of the Earth. Using color image processing, velocity fields at two horizontal cross-sections, one in each layer, of the vessel were measured simultaneously by stereoscopic particle image velocimetry to identify the interactions on interface between the layers. The temporal evolution of the velocity fields showed that thermal convection, first developed in the lower layer subsequently progresses ahead of the upper layer both with and without rotation. The rotation suppressed developments of convection in both of the two layers in cases of small thermal forces. The coupling structures of the 3D convection cells were evaluated from the perspectives of cross-correlations and the dominance ratio, representing the accumulation of the local couplings, by using simultaneously measured velocity information. The coupling structures were found to be well characterized by the dominance ratio, as various local couplings were coexisting in the 3D domain. The global coupling structures were in the thermal coupling, and those were weakened by the rotation.