Habitat corridors that facilitate functional connectivity are a fundamental component of wildlife conservation in fragmented landscapes. However, the landscape matrix separating suitable habitat is not uniformly impermeable to movement and management to increase matrix permeability could be an alternative means to maintain connectivity. Gliding mammals are particularly sensitive to fragmentation because their movements are constrained by glide distance thresholds. Populations of gliders in cities are at risk of being isolated by increasing habitat loss and urban development, yet little is known about how the urban matrix affects glider movement. Here we investigate how the level of urbanization and tree cover in the matrix influence matrix permeability to sugar gliders (Petaurus breviceps) within suburban forest reserves. Twenty-two sugar gliders were radio-tracked over winter and summer at four reserves. Boundary crossing behaviour was measured as the number of times each glider crossed into the matrix, and matrix permeability was determined as the maximum distance travelled by gliders into the matrix. The majority of gliders (81%) were located in the matrix at least once, and rates of boundary crossing were consistent across urbanization and tree cover levels. Matrix permeability was negatively affected by matrix urbanization, but not by matrix tree cover, and no interaction effects were found. Although distances travelled by gliders into the matrix did not exceed 180 m, they were comparable with typical movement distances by gliders in reserves. Our results demonstrate that the urban matrix can provide suitable habitat for gliding mammals to move and forage, but that increased urbanization may inhibit glider use of the matrix irrespective of tree cover. This finding has implications for conservation planning and suggests that structurally connected areas may not be used if movement behaviour is inhibited. Conversely, management of matrix permeability could be used to maintain connectivity without needing to construct physical corridors.