Abstract: Constructing 3D surfaces that interpolate 2D curves defined on parallel planes is a fundamental problem in computer graphics with wide applications including modeling anatomical structures. Typically the problem is simplified so that the 2D curves partition each plane into only two materials (e.g., air versus tissue). Here we consider the general problem where each plane is partitioned by a curve network into multiple materials (e.g., air, cortex, cerebellum, etc.). We present a novel method that automatically constructs a surface network from curve networks with arbitrary topology and partitions an arbitrary number of materials. The surface network exactly interpolates the curve network on each plane and is guaranteed to be free of gaps or self-intersections. In addition, our method provides a flexible framework for user interaction so that the surface topology can be modified conveniently when necessary. As an application, we applied the method to build a high-resolution 3D model of the mouse brain from 2D anatomical boundaries defined on 350 tissue sections. The surface network accurately models the partitioning of the brain into 17 abutting anatomical regions with complex topology.