Aims. Our goal is to identify bipolar H II regions and to understand their morphology, their evolution, and the role they play in the formation of new generations of stars. Methods. We use the Spitzer-GLIMPSE, -MIPSGAL, and Herschel-Hi-GAL surveys to identify bipolar H II regions, looking for (ionized) lobes extending perpendicular to dense filamentary structures. We search for their exciting star(s) and estimate their distances using near-IR data from the 2MASS or UKIDSS surveys. Dense molecular clumps are detected using Herschel-SPIRE data, and we estimate their temperature, column density, mass, and density. MALT90 observations allow us to ascertain their association with the central H II region (association based on similar velocities). We identify Class 0/I young stellar objects (YSOs) using their Spitzer and Herschel-PACS emissions. These methods will be applied to the entire sample of candidate bipolar H II regions to be presented in a forthcoming paper. Results. This paper focuses on two bipolar H II regions, one that is especially interesting in terms of its morphology, G319.88+00.79, and one in terms of its star formation, G010.32-00.15. Their exciting clusters are identified and their photometric distances estimated to be 2.6 kpc and 1.75 kpc, respectively; thus G010.32-00.15 (known as W31 north) lies much closer than previously assumed. We suggest that these regions formed in dense and flat structures that contain filaments. They have a central ionized region and ionized lobes extending perpendicular to the parental cloud. The remains of the parental cloud appear as dense (more than 10(4) cm(-3)) and cold (14-17 K) condensations. The dust in the photodissociation regions (in regions adjacent to the ionized gas) is warm (19-25 K). Dense massive clumps are present around the central ionized region. G010.32-00.14 is especially remarkable because five clumps of several hundred solar masses surround the central H II region; their peak column density is a few 10(23) cm(-2), and the mean density in their central regions reaches several 10(5) cm(-3). Four of them contain at least one massive YSO (including an ultracompact H II region and a high-luminosity Class I YSO); these clumps also contain extended green objects (EGOs) and Class II methanol masers. This morphology suggests that the formation of a second generation of massive stars has been triggered by the central bipolar H II region. It occurs in the compressed material of the parental cloud.< Réduire