Interval volumes are a generalization of isosurfaces that represent the set of points between two surfaces. In this paper, we present a compact multi-resolution representation for interval volume meshes extracted from regularly sampled volume data sets. The multi-resolution model is a hierarchical tetrahedral mesh whose updates are based on the longest edge bisection (LEB) subdivision strategy for tetrahedra. Although our representation is decoupled from the scalar field, it maintains the implicit structure of the LEB model to efficiently encode mesh updates. Our representation efficiently supports selective refinement queries and requires significantly less storage than an encoding of the interval volume mesh at full resolution.