Determining cost-effective transmission expansion plans in interconnected multi-region power systems requires a computationally tractable methodology that successfully characterizes major uncertainty sources and preserves the information privacy of regions (agents) reasonably. However, previous approaches usually fail to offer computational tractability and preserve privacy reasonably across different regions for multi-regional investment planning under uncertainty. To address these essential points, this paper first proposes a distributionally robust chance-constrained framework for transmission expansion planning (DR-TEP), which characterizes uncertainties of load demands and renewable power productions by a moment-based ambiguity set. The ambiguity set is constructed based on the first- and second-moment information and guarantees the robustness of the expansion plan against different probability distributions. Then, the alternating direction method of multipliers with a novel data exchange scheme is utilized to reformulate the proposed DR-TEP for each region with a central coordinator concerning local characteristics and interactions. The proposed information exchange is limited to power flows through existing and candidate inter-regional lines, Lagrangian multipliers, as well as output powers of thermal units to protect each region's privacy reasonably. Finally, three case studies on IEEE 24-bus and 118-bus test systems as well as the real-world Brazilian system validate the performance of the presented mathematical formulations.