As an auxiliary to the electricity market, the traditional frequency regulation market (FRM) lacks reliable data storage ways and direct transaction channels for buyers and sellers, and the cost-sharing method of frequency regulation (FR) service is still unfair. To this end, this article proposes a general and decentralized FRM framework based on multiblockchain techniques. According to the scheduling sequence of transactions, the FR services are divided mainly into before-the-fact transactions (BFTs) and after-the-fact transactions (AFTs). We construct a combinatorial double-auction model for BFTs and propose a novel cost-sharing model based on triggers for AFTs. Taking Pennsylvania-New Jersey-Maryland as an example, we design a consensus algorithm for the on-chain transaction process and cost sharing. Numerical results on both types of transactions show that the proposed auction model can meet the different needs of FR buyers. The proposed sharing method highlights that triggers from frequency events should result in higher costs. The consensus algorithm also improves the fault tolerance and throughput of transactions.