Most nonwoven fiber mats are produced with a uniform, narrow fiber diameter distribution. However, building evidence suggests that a bimodal diameter distribution (i.e., comprised of two populations of fibers, one with a smaller average diameter (d(av)), d, and the other with a larger d(av), D, where D >= 5d), has certain advantages in applications such as filtration media. To the best of our knowledge, all previous reports describing production of bimodal fiber diameter distributions have relied on solution-based electrospinning, a much less common fiber-spinning technique, compared to melt blowing, which currently produces more than 10% of nonwovens globally (an approximately $50 billion market). In this study, we demonstrate a facile method for producing bimodal fiber diameter distributions by melt blowing immiscible ternary polymer blends, with the two minority blend components being randomly dispersed as isolated, bimodally sized particles within the continuous matrix. Such a ternary blend can be obtained by selecting a matrix phase that preferentially wets/encapsulates both dispersed phases having vastly different viscosity ratios. Specifically, two model immiscible ternary blends comprised of polystyrene/polyethylene/Nylon-6 (PS/PE/Nylon) and poly(ethylene oxide)/polyethylene/Nylon-6 (PEO/PE/Nylon) with the desired morphologies and PS or PEO as the matrix were examined. During melt blowing of the blends, the PE minority domains (similar to 8 mu m in diameter) and Nylon minority domains (similar to 70 mu m in diameter) dispersed within the matrix were transformed to PE nanofibers (d(av) approximate to 560 nm) and Nylon microfibers (d(av) approximate to 8 mu m) embedded in the elongated PS matrix fibers, and similarly for fibers made with a PEO matrix. Subsequent removal of the matrix polymer with an appropriate solvent (tetrahydrofuran for PS or water for PEO) produced a macroscopic mat of randomly distributed, bimodal nanofibers and microfibers. The nanofiber and microfiber compositions of the bimodal-diameter fiber mats were effectively tuned by varying the composition of the minority components of the original ternary polymer blends. Interestingly, the resulting bimodal-diameter fiber mats possessed few nanofiber bundles; we hypothesize that this is due to the presence of Nylon microfibers that are intrinsically intermixed among the PE nanofibers that physically restrict the formation of nanofiber bundles. Overall, this versatile method could provide a high-throughput route to scalable quantities of fiber mats with a bimodal distribution of fiber diameters, thus promoting the application of hierarchically structured nonwovens.