In this paper, a multi-objective mixed integer linear programming (MOMILP) approach is proposed for the optimal planning of battery energy storage systems (BESSs) and the interlink converter (ILC) in hybrid AC/DC microgrids (HMGs). The ILC is the backbone of the HMG, facilitating power exchange between the sub-grids. It plays a vital role in enhancing the stability of the HMG by balancing power between subsystems. Economically, the ILC enables the transfer of surplus power and lower-cost energy between the AC and DC microgrids. Therefore, selecting an optimal size for the ILC is critical from both technical and economic perspectives. However, existing studies have overlooked the optimal sizing of the ILC and its associated stress factors in the planning of HMGs. This paper proposes a multi-objective planning approach for HMGs that considers both calendar and cyclic ageing of BESSs. The performance of the proposed strategy is compared with the most widely used existing methods. The results confirm the superiority of the proposed planning approach in terms of both technical performance and economic efficiency.