In this work, the semi-grand statistical ensemble formalism proposed by Pant and Theodorou (Macromolecules, 1995, 28, 7224) for polydisperse melts of linear chains is extended to mixtures of linear and branched chains in order to calculate stability of binary polymer blends based on Monte Carlo simulation. Furthermore, a new elementary Monte Carlo move is introduced 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, are shown to relax efficiently both the branched and the linear molecules in binary linear polyethylene-triarm polyethylene blends of various macromolecular sizes. Subsequently, they are used for the calculation of the microscopic structure and the thermodynamic properties of these systems. All blends examined are shown to be fully miscible.