Polymer blends are important materials both from the scientific as well as from the industrial point of view. The accurate knowledge of their thermodynamic properties is crucial for the optimal design and use of these materials. In this work, a new semi-grand statistical ensemble formalism is proposed that allows calculation of stability of binary polymer blends based on Monte Carlo simulation. Furthermore, a new elementary Monte Carlo move is proposed that consists of chain identity-altering between branched and linear chain species and thus allows fluctuations in the blend composition. The new move, together with previously developed moves for long chain molecules (both linear and branched), are shown to relax efficiently both the branched and the linear molecules in binary linear polyethylene – tri-arm polyethylene blends of various macromolecular sizes. Subsequently, these moves are used for the calculation of the microscopic structure and the thermodynamic properties of various blends. The effect of chain and arm molecular weight and of temperature is examined. Chemical potential versus composition diagrams are drawn in order to assess the non-ideality of mixing that may lead to phase separation. All of the blends examined but one are shown to be fully miscible. A blend consisting of a relatively short linear component and a much longer symmetric tri-arm component exhibits a much different chemical potential – composition behavior, indicative of a partially miscible system. The microscopic blend structure is examined by calculating the radial distribution function. Finally, the radii of gyration of linear and branched chains are calculated and scaling exponents are evaluated.