Multi-energy systems (MESs) involve the synergetic operation of different energy vectors, unlocking higher system flexibility and efficiency. Nonetheless, they suffer from high model complexity, large-scale dimension, and different dynamical transient time constants. Moreover, each energy vector may have its own stakeholder, raising privacy concerns. In this framework, this article proposes a distributed two-layer predictive control architecture enabling to solve the mentioned issues. The lower level consists of decentralized Model Pre-dictive Control (MPC) regulators considering detailed models, possibly nonlinear, while the high level exploits a convex and unified energy modelling of each energy vector using a fully distributed algorithm named Dual Consensus ADMM (DC-ADMM). The proposed control architecture is tested on an extended case study composed of three interconnected energy vectors i.e., a hydrogen energy system, a district heating network from the literature, and the IEEE 37-bus power system, showing promising results.