The magnetic property of a 0.7BiFeO3-0.3TbMnO3 composite has been studied in detail and compared with that of 0.8BiFeO3-0.2TbMnO3. The magnetic properties in 0.7BiFeO3-0.3TbMnO3 are improved in manifold compared to BiFeO3. An exchange bias (HEB) is observed in both the compositions of these antiferromagnetic composites, which varies between 5 and 180 Oe with a maximum at ∼275 K. Isothermal remanent magnetization measurements at room temperature indicate the presence of an interfacial layer of a 2-dimensional dilute uniaxial antiferromagnet in a uniform magnetic field (2D DAFF). The presence of exchange bias can be explained on the basis of a strong strain-mediated magnetoelectric coupling induced exchange interaction and the creation of a 2D DAFF layer at the interface. The properties of this layer are defined by canting and pinning of BiFeO3 spins at the interface with TbMnO3 due to Fe and Mn interaction. X-ray magnetic circular dichroism confirms the presence of canted antiferromagnetic ordering of BiFeO3, charge transfer between Mn ions, and different magnetically coupled layers that play a vital role in the exchange bias. © 2019 Author(s).