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Gaseous, disc–halo interfaces are shaped by processes that are critical to galaxy evolution, including gas accretion and outflows. Extraplanar diffuse ionized gas (eDIG) layers are characterized by scale heights that largely exceed those predicted by their temperature, suggesting the presence of turbulent energy injection from star-formation feedback. However, the origin of this large-scale height remains uncertain. To explore the connection between eDIG and star-forming discs, we present a spatially resolved case study of a nearby pair of sub- |$L_*$|⁠ , intermediately inclined disc galaxies NGC 3511/3513. We decompose optical nebular lines observed using long-slit spectroscopy into narrow and broad velocity components. In NGC 3511, the broad component has three distinctive characteristics in comparison to the narrow component: (1) significantly higher velocity dispersions (a median |$\langle \sigma \rangle _{\text{Broad}} = 24$|  km s |$^{-1}$| compared to |$\langle \sigma \rangle _{\text{Narrow}} = 13$|  km s |$^{-1}$|⁠), (2) elevated [N  ii ] |$\lambda$| 6583/H |$\alpha$| and [S  ii ] |$\lambda$| 6716/H |$\alpha$| line ratios, and (3) a rotational velocity lag. These characteristics support the origin of the broad component in an extraplanar, gaseous disc. In NGC 3513, the broad component reveals disc–halo circulation via localized outflows at radius |$\lesssim 1$|  kpc. For NGC 3511, we test a vertical hydrostatic equilibrium model with pressure support supplied by thermal and turbulent motions. Under this assumption, the eDIG velocity dispersion corresponds to a scale height |$h_{z} \gtrsim 0.2 - 0.4$|  kpc at |$R = 3 - 5$|  kpc, a factor of a few above the thermal scale height (⁠|$h_{z} \lesssim 0.1$|  kpc). This highlights the importance of turbulent motions to the vertical structure of the gaseous, disc–halo interface. [ABSTRACT FROM AUTHOR]