Most industrial practices for turning power into hydrogen face a similar challenge, i.e., hydrogen consumption. One solution is injecting hydrogen into the existing natural gas (NG) infrastructure, so as to enter the market without expensive investments. However, a major concern regarding HCNG (Hydrogen enriched compressed natural gas) is the amount of hydrogen that can be added to the natural gas infrastructure without any modification. The current studies have focused on the modeling of HCNG components under various H2 fractions, but there is a lack of research on the system operation of HCNG, especially when incorporated with dispersed renewables and CHP plants. To fill in the gaps from the component to the system level, this paper proposes a comprehensive HCNG operation model coupled with the operations of an electrical and heating network. Via this model, the system performance incorporated with HCNG distribution networks could be studied under various H2 fractions and HCNG load portfolios (HLP). The numerical studies demonstrate the benefits of integrating the HCNG distribution network, especially in terms of local balancing of distributed generators and minimizing the operational costs.