A bilayer surface model of human atria is presented. A rule-based bi-layer physiological fibre arrangement is defined on an imaged in-vivo atrial geometry. This fibre architecture includes the main structures of fibres in the right and left atria, including the main transmural heterogeneities and transseptal connexions. The precision of the corresponding bilayer mathematical model is assessed by comparing the case of two sheets of orthogonal fibres to a three dimensional slab of tissue. A comparison of bilayer and monolayer simulations of sinus propagation is finally proposed. This model allows inclusion of transmural heterogeneities while maintaining small computational costs associated with surface models. It then proposes a good trade-off between model precision and computing efforts for performing complex atrial simulations for a clinical use.