We present a micromagnetic model for NiFe-TbCo exchange coupled bilayers that can quantitatively predict and explain the major macroscopic features observed in measured M-H characteristics. Comparison of theoretical and experimental results shows conclusively that the strong interfacial exchange coupling in NiFe-TbCo is essentially indistinguishable from that of a perfect, homogeneous interface. Commonly invoked assumptions concerning the existence or origin of a grossly weakened exchange coupling at a highly imperfect interface are neither necessary nor consistent with experimental measurements. The mechanism of the unidirectional exchange anisotropy is the formation of Bloch-type domain walls in a approximately-equal 0.08-mu-m-thick TbCo sublayer of uniaxial, in-plane anisotropy adjacent to the NiFe interface. The manner in which the observable magnetic behavior of NiFe-TbCo bilayers depends on film thicknesses, TbCo anisotropy, interfacial exchange coupling strength, as well as the previously unconsidered large hysteretic effects due to the small net magnetization in ferrimagnetic TbCo, are discussed in detail. It is demonstrated, for a strongly coupled system such as NiFe-TbCo, that the often used single parameter "exchange field" description of a shifted NiFe M-H loop is inadequate. A quantitatively accurate description requires that one take into account the spatial variations in the micromagnetic magnetization distributions of both layers.