Based on experimental data on the newly synthesized iron-based superconductors and the relevant band structure calculations, we propose a minimal two-band BCS-type Hamiltonian with the interband Hubbard interaction included. We illustrate that this two-band model is able to capture the essential features of unconventional superconductivity and spin density wave (SDW) ordering in this family of materials. It is found that bound electron-hole pairs can be condensed to reveal the SDW ordering for zero and very small doping, while the superconducting ordering emerges at small finite doping, whose pairing symmetry is qualitatively analyzed to be of nodal d-wave. The derived analytical formulas not only give out a nearly symmetric phase diagram for electron and hole doping, but also is likely able to account for existing main experimental results. Moreover, we also derive two important relations for a general two-band model and elaborate how to apply them to determine the band width ratio and the effective interband coupling strength from experimental data.PACS numbers: 74.20. Rp, 75.30.Fv, 74.25.Bt Since the recent discovery of a new iron-based layered superconductor [1], intensive efforts have been focused on the nature of superconductivity in this materials both experimentally [2,3,4,5,6,7,8,9,10,11,12] and theoretically [13,14,15,16,17,18,19,20,21]. Apart from the well-known copper oxide superconductors, this family of materials exhibit higher critical temperatures, 26K in LaO 0.9 F 0. performed angle-integrated photoemission spectroscopy measurements and their data provided certain support for the existence of SDW ordering and an indication of unconventional superconductivity. In the theoretical aspect, the nature of unconventional superconductivity and the pairing mechanism have also been explored preliminarily by several groups based on the density functional theory (DFT) and dynamic mean filed theory (DMFT) [15,16,17,18,19]. It was pointed out that the electron-phonon interaction in this system may be too weak to lead such high critical temperatures [20]. The possibility of spin triplet superconductivity was also suggested [21,22].In this paper, we propose a minimal two-band BCStype Hamiltonian with an effective interband Hubbard interaction term included to model the system. The construction of our model Hamiltonian is based on band structure calculation results and intuitive physical pictures. Taking into account the main features of fermi surface for the undoped material calculated from the DFT and to capture the essential physics of the superconductivity and magnetism in the present system, we adopt a minimal version of the Fermi surface on a primary twodimensional square lattice in the Fe-Fe plane: one hole band around Γ and one electron band around M points, both crossing the Fermi surface in the undoped case. Based on rational physical considerations, we introduce an effective interband antiferromagnetic interaction and elucidate that the effective intraband antiferromagnetic coupling could induce th...