Biological membranes are versatile in composition and host intriguing molecular processes. In order to be able to study these systems, an accurate model Hamiltonian or force field (FF) is a necessity. Here, we report the results of our extension of earlier developed all-atomistic FF parameters for fully saturated phospholipids that complements an earlier parameter set for saturated phosphatidylcholine lipids (J. Phys. Chem. B, 2012, 116, 3164-3179). The FF, coined Slipids (Stockholm lipids), now also includes parameters for unsaturated phosphatidylcholine and phosphatidylethanolamine lipids, e.g., POPC, DOPC, SOPC, POPE, and DOPE. As the extended set of parameters is derived with the same philosophy as previously applied, the resulting FF has been developed in a fully consistent manner. The capabilities of Slipids are demonstrated by performing long simulations without applying any surface tension and using the correct isothermal-isobaric (NPT) ensemble for a range of temperatures and carefully comparing a number of properties with experimental findings. Results show that several structural properties are very well reproduced, such as scattering form factors, NMR order parameters, thicknesses, and area per lipid. Thermal dependencies of different thicknesses and area per lipid are reproduced as well. Lipid diffusion is systematically slightly underestimated, whereas the normalized lipid diffusion follows the experimental trends. This is believed to be due to the lack of collective movement in the relatively small bilayer patches used. Furthermore, the compatibility with amino acid FFs from the AMBER family is tested in explicit transmembrane complexes of the WALP23 peptide with DLPC and DOPC bilayers, and this shows that Slipids can be used to study more complex and biologically relevant systems.