Modeling tools typically have their own interaction methods for combining virtual objects. For realistic composition in 3D space, many researchers from the fields of virtual and augmented reality have been trying to develop intuitive interactive techniques using novel interfaces. However, many modeling applications require a long learning time for novice users because of unmanageable interfaces. In this paper, we propose two-handed tangible augmented reality interaction techniques that provide an easy-to-learn and natural combination method using simple augmented blocks. We have designed a novel interface called the cubical user interface, which has two tangible cubes that are tracked by marker tracking. Using the interface, we suggest two types of interactions based on familiar metaphors from real object assembly. The first, the screw-driving method, recognizes the user's rotation gestures and allows them to screw virtual objects together. The second, the block-assembly method, adds objects based on their direction and position relative to predefined structures. We evaluate the proposed methods in detail with a user experiment that compares the different methods.