Context It is already accepted that Be stars are surrounded by circumstellar envelopes, which are mostly compatible with a disc geometry in Keplerian rotation. Their infrared region is characterised by a moderate flux excess and the presence of hydrogen recombination lines that allow us to obtain information on the physical and dynamical structure of different regions inside the disc. Nevertheless, many of the infrared studies available in the literature show low-resolution spectra, or are restricted to a small object sample or describe just an individual object. Some others analyse reduced spectral ranges or just one infrared band. Aims We aim to obtain a more complete characterisation of the properties of the circumstellar environment of Be stars that helps to constrain the theoretical models of the Be phenomenon. Methods Throughout the last decade, we used the spectroscopic facilities at the Gemini and Las Campanas observatories to obtain quasi-simultaneous spectra in the J, H, K, and L bands of a sample of Be stars with medium resolution. Results We present near-infrared, medium-resolution spectra of a sample of galactic Be stars with different spectral subtypes and luminosity classes. We measure different parameters of the hydrogen recombination lines from the Paschen, Brackett, Pfund, and Humphreys series, and use them to diagnose physical conditions in the circumstellar environment. We analysed the equivalent-width (EW) ratio between Brα and Brγ lines and different diagrams of flux ratios. We also identify lines from He i , C i , N i , O i , Na i , Mg i , Mg ii , Si i , Fe i , and Fe ii . Analysing the EW measurements of particular He i , Mg ii , Fe i , Fe ii and O i lines, we find that for some lines they correlate with the spectral type of the star. Particularly, the emission of the O i λ 1.3168 μm line decreases towards the later spectral types. Conclusions We present an atlas of 22 Be stars, that covers a wide infrared (IR) spectral range with quasi-simultaneous observations. From a detailed analysis, we define new complementary criteria to Mennickent’s classification of Be stars according to their disc opacity. Some objects in our sample present compact thick envelopes, while in others the envelope is extended and optically thin. The correlation between the full widths at half maximum and the peak separation (ΔV) versus V sin i for the Br10, Brδ, and Hu14 lines reveals that the broadening mechanism is rotational. The Lyβ fluorescence is a key mechanism to explain the intensity of the emission of Mg ii and O i lines.