Multiple interconnected ac and dc microgrids (MGs) are being studied by academia and industry because of their benefits despite their operational challenges. Coordinating distributed generators (DGs) is complex, so communication-based controllers are proliferating in the literature. Then, this work proposes a distributed control strategy for islanded ac/dc multi-MGs interconnected by interlinking converters (ILCs). The proposed scheme is implemented in the ILCs and consists of distributed controllers that equalize global generation costs, allowing secondary control in each MG. Control actions that safeguard the saturated operation of MGs and ILCs are included in the control designs. The simultaneous operation with multiple objectives is possible due to adjusting control parameters according to a prioritization criterion. Experiments are conducted through an extensive simulated environment. The results show the proposed multiobjective controllers could maintain global optimal costs during normal operation while not overloading DGs, ILCs, subgrids, and clusters of ILCs. Furthermore, the strategy may reduce operational costs in the long term by protecting the lifetime of critical MG components. Desynchronization of incremental costs is enforced at 15% at most under demanding conditions. Also, it is possible to operate against considerable (>250 [ms]) time delays in the tests.