This paper investigates the coordinated power sharing issues of interlinked ac/dc microgrids. An appropriate control strategy is developed to control the interlinking converter (IC) to realize proportional power sharing between ac and dc microgrids. The proposed strategy mainly includes two parts: 1) the primary outer-loop dual-droop control method along with secondary control; and 2) the inner-loop data-driven model-free adaptive voltage control. Using the proposed scheme, the IC, just like the hierarchical controlled distributed generator units, will have the ability to regulate and restore the dc terminal voltage and ac frequency. Moreover, the design of the controller is only based on input/output measurement data, but not the model any more, and the system stability can be guaranteed by the Lyapunov method. The detailed system architecture and proposed control strategies are presented in this paper. Simulation and experimental results are given to verify the proposed power sharing strategy.