In the emerging electricity market, bilateral transactions are conducted between distribution-grid operators and micro-grid operators. Under the uncertainty caused by the large-scale integration of wind and solar generation, the cooperation game between the distribution-grid and the micro-grid is analyzed at the planning level. The impact of multi-agent bilateral energy transactions is considered in this approach. To address the multiple non-convexities in traditional coordinated planning of distribution-grid and micro-grid, an alternating optimization-based strategy is proposed. Through the alternating optimization process, the discontinuous coordinated planning problem is transformed into a bi-level iterative solving process. In the upper level, Nash bargaining is applied to determine the traded electricity and payment strategies within a convex subset generated by the lower level. In the lower level, local individual planning problems are solved using trading variables obtained from the upper level. The market-clearing problem is decomposed into two subproblems, electricity transaction and payment settlement. The alternating direction method of multipliers is used sequentially to solve these subproblems. Case simulations on the IEEE 33-bus system demonstrate that the proposed model effectively enhances the operational benefits for both trading parties.