For the applications of the frequency comb in microresonators, it is essential to obtain a fully frequency-stabilized microcomb laser source. In this study, we present a system for generating a fully atom-referenced stabilized soliton microcomb. The pump light around 1560.48 nm is locked to an ultra-low-expansion (ULE) cavity. This pump light is then frequency-doubled and referenced to the atomic transition of 87Rb. The repetition rate of the soliton microcomb is injection-locked to an atomic-clock-stabilized radio frequency (RF) source, leading to mHz stabilization at 1 s. As a result, all comb lines have been frequency-stabilized based on the atomic reference and the ULE cavity, achieving a very high precision of approximately 18 Hz at 1 s, corresponding to the frequency stability of 9.5 x 10-14. Our approach provides a fully stabilized microcomb experiment scheme with no requirement of f-2f technique, which could be easily implemented and generalized to various photonic platforms, thus paving the way towards the ultraprecise optical sources for high precision spectroscopy.