We have studied the equilibrium structure of a grafted polymer layer composed of two distinct species of homopolymers, the "binary brush", in various solvent conditions. By using a coarse-grained simulation method that involves direct calculation of the Edwards hamiltonian, we are able to simulate much larger systems than would otherwise be possible with a more standard lattice simulation. If the two species are made sufficiently immiscible, we find lateral binary microphase separation over a wide range of solvent conditions. Due to the presence of solvent, we find a stage where the brush expands in a laterally homogeneous manner as immiscibility increases. In this stage, laterally averaged quantities are well-described by a single solvent-related parameter : a modified excluded volume parameter. This is followed by lateral microphase separation in which the brush volume remains relatively constant. In Theta solvent, this phase separation sets in at a degree of immiscibility consistent with a mean field prediction for melt layers. The onset of phase separation is delayed as solvent quality increases. Furthermore, a reduction in solvent quality results in a stronger crossover between mixed and phase-separated configurations. Under poor solvent conditions, we find interesting structural variations as a result of the combination of phase separation from solvent and phase separation of the two species.