A general model of a hybrid interfacial domain wall (HIDW) in ferromagnetic/antiferromagnetic exchange biased bi-layers is proposed, where an interfacial domain wall is allowed to extend into either the ferromagnetic or antiferromagnetic layer or across both. The proposition is based on our theoretical investigation on thickness and field dependences of ferro-magnetic domain wall (FMDW) and antiferromagnetic domain wall (AFDW), respectively. Good match of the simulation to the hysteresis loops of a series of NiFe/FeMn exchange-biased bilayers confirms the existence of the HIDW, where the AFDW part is found to preferentially occupy the entire antiferromagnetic layer while the FMDW shrinks with the increased magnetic field as expected. The observed asymmetry between the ascending and descending branches of the hysteresis loop is explained naturally as a consequence of different partition ratios between AFDW and FMDW.