The complex structure of gas, metals, and dust in the interstellar and circumgalactic medium (ISM and CGM, respectively) in star-forming galaxies can be probed by Ly$alpha$ emission and absorption, low-ionization interstellar (LIS) metal absorption, and dust reddening E(B-V). We present a statistical analysis of the mutual correlations among Ly$alpha$ equivalent width (EW$_{Lyalpha}$), LIS equivalent width (EW$_{LIS}$), and E(B-V) in a sample of 157 star-forming galaxies at $zsim2.3$. With measurements obtained from individual, deep rest-UV spectra and spectral-energy distribution (SED) modeling, we find that the tightest correlation exists between EW$_{LIS}$ and E(B-V), although correlations among all three parameters are statistically significant. These results signal a direct connection between dust and metal-enriched HI gas, and that they are likely co-spatial. By comparing our results with the predictions of different ISM/CGM models, we favor a dusty ISM/CGM model where dust resides in HI gas clumps and Ly$alpha$ photons escape through the low HI covering fraction/column density intra-clump medium. Finally, we investigate the factors that potentially contribute to the intrinsic scatter in the correlations studied in this work, including metallicity, outflow kinematics, Ly$alpha$ production efficiency, and slit loss. Specifically, we find evidence that scatter in the relationship between EW$_{Lyalpha}$ and E(B-V) reflects the variation in metal-to-HI covering fraction ratio as a function of metallicity, and the effects of outflows on the porosity of the ISM/CGM. Future simulations incorporating star-formation feedback and the radiative transfer of Ly$alpha$ photons will provide key constraints on the spatial distributions of neutral hydrogen gas and dust in the ISM/CGM structure.
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