This paper proposes a fuzzy chance-constrained fractional programming (FCFP) method for planning distributed multi-energy systems (DMES). FCFP can deal with uncertainties expressed as fuzzy information, probability distributions, and multiple objectives. The FCFP-DMES model was applied to a real airport in a case study, and a series of scenarios were selected to examine the effects of the uncertainty on the energy supply and technology selection. Additionally, a comparison related to conventional energy system (CES) and DMES are discussed from energy consumption, economic, and environmental aspects. The results revealed the following: the combined cooling, heat, and power would serve as a primary distributed energy resource providing heating, cooling, and electricity in different seasons, accounting for approximately 40% of the total; among different alternative technologies, heating supplied by gas-fired boiler and thermal storage would serve as auxiliary heaters to cover 6.6% and 15.2% of the heating load, respectively, under high-level demand; although the DMES cannot bring cost-cutting, it has better environmental performance and a peak shaving function. Compared with the DMES, the CES would almost double the electricity purchasing cost (reaching $9.56 million), and an additional 136.24 MW of electricity would be needed, which would result in 127.5 tons/year of pollutant emissions. The findings of this study indicate that the FCFP-DMES model can provide a comprehensive and systematic strategy considering the multi-energy, multi-technology, and multi-uncertainty within the DMES.