Facing the dilemma of mitigating carbon emissions and growing energy demand, this paper proposes a hierarchical electricity-carbon trading mechanism for virtual federated prosumers (VFPs) in regional markets. At the inter-regional level, a trading platform coordinates the energy-sharing and wholesale markets, intending to minimize the cost of VFPs. The clearing of the energy-sharing market is formulated as a non-cooperative game, in which a flow-based distributed consensus algorithm is developed to obtain equilibrium with limited shared information. On the other hand, at the intra-regional level, each VFP as selfless auctioneer leverages discriminatory weights and benchmark prices to allocate the electricity-carbon budget intra-VFP (i.e., among the prosumer nodes within the VFP) and to maximize social welfare, for which a distributed feedback allocation algorithm is proposed. The hierarchical electricity-carbon trading is solved by a progressive alternate iterative algorithm. A case study based on a practical regional grid verifies the effectiveness of the proposed algorithms and shows that the mechanism improves energy efficiency and reduces carbon emissions.