The composite cytoskeleton, comprising interacting networks of semiflexible actin filaments and rigid microtubules, restructures and generates forces using motor proteins such as myosin II and kinesin to drive key processes such as migration, cytokinesis, adhesion, and mechanosensing. While actin-microtubule interactions are key to the cytoskeleton's versatility and adaptability, an understanding of their interplay with myosin and kinesin activity is still nascent. This work describes how to engineer tunable three-dimensional composite networks of co-entangled actin filaments and microtubules that undergo active restructuring and ballistic motion, driven by myosin II and kinesin motors, and are tuned by the relative concentrations of actin, microtubules, motor proteins, and passive crosslinkers. Protocols for fluorescence labeling of the microtubules and actin filaments to most effectively visualize composite restructuring and motion using multi-spectral confocal imaging are also detailed. Finally, the results of data analysis methods that can be used to quantitatively characterize non-equilibrium structure, dynamics, and mechanics are presented. Recreating and investigating this tunable biomimetic platform provides valuable insight into how coupled motor activity, composite mechanics, and filament dynamics can lead to myriad cellular processes from mitosis to polarization to mechano-sensation.