Accurate chemical compositions of star-forming regions provide a critical diagnostic tool for characterizing the star formation history and gas flows that regulate galaxy formation. However, the abundance discrepancy factor (ADF) between measurements derived from the “direct” optical electron temperature (Te) method and those from recombination lines (RLs) introduces a ∼0.2 dex systematic uncertainty in the oxygen abundance. The degree of uncertainty for other elements is unknown. We conduct a comprehensive analysis of O++ and N+ ion abundances using optical and far-infrared (far-IR) spectra of a star-forming region within the nearby dwarf galaxy Haro 3, which exhibits a typical ADF. Assuming homogeneous conditions, the far-IR emission indicates an oxygen abundance higher than that derived using the Te method and consistent with the RL value, as expected from temperature fluctuations, whereas the far-IR nitrogen abundance is too large to be explained by temperature fluctuations. A two-phase analytical model reveals that differential dust obscuration associated with temperature inhomogeneity is likely required to explain all the emission-line ratios, and that the total oxygen metallicity of two phases is consistent with the RL metallicity. Our findings underscore the critical importance of resolving the cause of abundance discrepancies and understanding the biases between different metallicity methods. This work presents a promising methodology, and we identify further approaches to address the dominant sources of uncertainty.