We present a near-infrared spectro-interferometric observation of the non-Mira-type, semiregular asymptotic giant branch star SW Vir. Our aim is to probe the physical properties of the outer atmosphere with spatially resolved data in individual molecular and atomic lines. We observed SW Vir in the spectral window between 2.28 and 2.31 micron with the near-infrared interferometric instrument AMBER at ESO's Very Large Telescope Interferometer (VLTI). Thanks to AMBER's high spatial resolution and high spectral resolution of 12000, the atmosphere of SW Vir has been spatially resolved not only in strong CO first overtone lines but also in weak molecular and atomic lines of H_2_O, CN, HF, Ti, Fe, Mg, and Ca. While the uniform-disk diameter of the star is 16.23+/-0.20mas in the continuum, it increases up to 22-24mas in the CO lines. Comparison with the MARCS photospheric models reveals that the star appears larger than predicted by the hydrostatic models not only in the CO lines but also even in the weak molecular and atomic lines. We found that this is primarily due to the H2O lines (but also possibly due to the HF and Ti lines) originating in the extended outer atmosphere. Although the H_2_O lines manifest themselves very little in the spatially unresolved spectrum, the individual rovibrational H_2_O lines from the outer atmosphere can be identified in the spectro-interferometric data. Our modeling suggests an H_2_O column density of 10^19^-10^20^cm^-2^ in the outer atmosphere extending out to ~2R*. Our study has revealed that the effects of the nonphotospheric outer atmosphere are present in the spectro-interferometric data not only in the strong CO first overtone lines but also in the weak molecular and atomic lines. Therefore, analyses of spatially unresolved spectra, such as for example analyses of the chemical composition, should be carried out with care even if the lines appear to be weak.