This paper presents the planning of solar photovoltaics (PV), battery energy storage system (BESS) and gas-fired micro turbine (MT) in a coupled micro gas and electricity grid. The proposed model is formulated as a two-stage stochastic optimization problem, including the optimal investment in the first stage and the optimal operation in the second stage. To better understand the mutual interactions between electric and heat energy, the gas network models are taken into account. As a result, the fuel availability and price of the gas-fired MT can be explicitly modeled and analyzed. Moreover, to enhance the computational efficiency of the formulated mixed-integer quadratic programming problem, the point estimation method is used as the scenario reduction technique. The effectiveness of the proposed model is verified on a 14-bus coupled micro energy grid. Based on the case studies, the proposed two-stage planning model can identify a planning solution with the objective value of $99.3104, which is comprised of the daily capital recovery cost of $20.5070, the daily operating cost of $78.8034 for the coupled micro gas and electricity grid. Comparative studies demonstrate that the proposed approach can help the microgrid operator identify feasible and optimal planning solutions, and provide valuable guidance for energy infrastructure expansion from an integrated perspective.