This work studied the thermal conductance of thin layers with randomly oriented composites by the percolation theory, and developed an effective-medium approximation (EMA) model for triple bond percolation systems. The results showed that the thin layer is anisotropic in conductivities when its thickness is lower than the correlation length. The conductivity in normal direction increases with decreasing thickness while the in-plane conductivity declines. The significance of this thickness effect is a function of the concentration of good conductor and the thermal conductivity ratio of the phases in the composites. A threshold concentration exists for the conductivity of bulk composites, beyond which the effective thermal conductivity increases significantly from that of the poor conductor with increasing concentration. The developed EMA model agrees quite well with the numerical simulation and is expected being applicable to predict thermal conductivities of composites using the coordination number as a fitting parameter