We present a multiwavelength study of two southern Galactic H II regions G346.056-0.021 and G346.077-0.056 which are located at a distance of 10.9kpc. The distribution of ionized gas, cold and warm dust, and the stellar population associated with the two H II regions are studied in detail using measurements at near-infrared, mid-infrared, far-infrared, submillimeter and radio wavelengths. The radio continuum maps at 1280 and 610MHz were obtained using the Giant Metrewave Radio Telescope to probe the ionized gas. The dust temperature, column density, and dust emissivity maps were generated using modified blackbody fits in the far-infrared wavelength range 160-500um. Various near- and mid-infrared color and magnitude criteria were adopted to identify candidate ionizing star(s) and the population of young stellar objects in the associated field. The radio maps reveal the presence of diffuse ionized emission displaying distinct cometary morphologies. The 1280MHz flux densities translate to ZAMS spectral types in the range O7.5V-O7V and O8.5V-O8V for the ionizing stars of G346.056-0.021 and G346.077-0.056, respectively. A few promising candidate ionizing star(s) are identified using near-infrared photometric data. The column density map shows the presence of a large, dense dust clump enveloping G346.077-0.056. The dust temperature map shows peaks towards the two HII regions. The submillimeter image shows the presence of two additional clumps, one being associated with G346.056-0.021. The masses of the clumps are estimated to range between ~1400 and 15250M_{sun}_. Based on simple analytic calculations and the correlation seen between the ionized gas distribution and the local density structure, the observed cometary morphology in the radio maps is better explained invoking the champagne-flow model.