The exchange between the hard and soft layer in the exchange coupled composite (ECC) medium is crucial for the recording performance. An accurate micromagnetic model is built for Co-TiO2 (4 nm)/Pt(delta=0-2.8 nm)/CoPt-TiO2 (16 nm) ECC media, based on the microstructure, to investigate the magnetic parameters such as the exchange constant A*(3) between the soft/hard layer. In the M-H loops of CoPt-TiO2(16 nm) hard layer, the perpendicular coercivity is 6.1 kOe and the squareness S is 0.98. In ECC media, the thickness delta of interlayer Pt has comprehensive effects on magnetic properties: the coercivity and squareness change little when we just vary A*(3) or delta; A*(3) equals the intragrain exchange constant A*(1) when delta is thinner than grain boundary (<= 2 nm); and A*(3) decreases from the intergrain exchange constant A* (2) to 0 when delta increases from 2.2 to 2.8 nm. The simulation results agree well with experiments. (C) 2012 American Institute of Physics. [doi:10.1063/1.3679450]