We demonstrate a practical mid-infrared (MIR) dual-comb spectroscopy (DCS) method based on a bidirectional dual-comb fiber laser. By exploiting the inherently high relative stability and mutual coherence of the dual-comb laser, we stabilize the MIR dual-comb modes with sufficient precision using only piezoelectric control of the repetition frequencies. This simple configuration enables correction of residual timing jitter and phase noise in interferograms while preserving the absolute optical frequency scale defined by the experimentally obtained comb parameters, without requiring an external continuous-wave laser reference or tight phase-locking. Importantly, the proposed method does not merely produce apparently clean interferograms through signal processing, but enables coherent averaging while retaining both the physically meaningful interferometric waveforms and well-defined absolute frequency information. The proposed system is experimentally validated through MIR spectroscopy of N₂O around 3.9 μm, achieving a signal-to-noise ratio of approximately 690 through coherent averaging of 10,000 interferograms over 65 s, along with the acquisition of an absorption spectrum consistent with the reference data. These results demonstrate a simple and practical approach to absolute-frequency-referenced MIR-DCS.