Frustrated interactions in the Cu-based mineral rouaite with alternating antiferromagnetic and ferromagnetic spin chains, Cu2(OH)3NO3, introduce non-trivial magnetic ground states and exotic excitations arising from them. We investigated the magnetic structure of Cu2(OH)3NO3 by 1H- and 2H-NMR measurements on single crystals. The internal fields in the ordered state were microscopically measured using the H nuclear moments as a local probe. The directions of the ordered moments were determined by comparing the experimental results to model calculations. The obtained magnetic structure suggests the importance of Dzyaloshinskii–Moriya interactions in stabilizing the low-field magnetic structure. The present result advances the theoretical understanding of the low-field magnetic states and will enable exploration of the exotic magnetic states emerging in high magnetic fields.