We have developed a new density functional theory (DFT) to describe phase behavior and microstructure of mixtures of polymeric fluids in inhomogeneous environments. The theory is based on Wertheim's thermodynamic perturbation theory for association; it treats the polyatomic system as a mixture of strongly associating monomers, and invokes the limit of complete association in the free energy functional. The theory is formulated in terms of segment density; therefore it offers the simplicity and computational efficiency of an atomic DFT. This feature of iSAFT makes it best suited for modeling interfacial properties and structure of chains of several hundreds or even thousands of segments. We demonstrate the success of the theory in capturing the effects of size and shape of the fluid molecules and system parameters such as fluid-fluid and surface-fluid interaction strengths on fluid structure and interfacial properties. Our DFT shares a common basis with the Statistical Associating Fluid Theory (SAFT), one of the most accurate and widely used theories for bulk polymer solutions. This self-consistency of the bulk and interfacial models is crucial; it enables us to predict the interfacial properties of the considered systems with a set of molecular parameters obtained from the readily available bulk properties. We compare results from iSAFT to molecular simulations, as well as experimental data for interfacial tension and molecular structure of realistic systems comprising polymer melts, blends and solutions.