The sodium iron phosphite NaFe3(HPO3)(2)(H2PO3)(6) is studied by ac-magnetic susceptibility, pulsed-field magnetization, specific heat, and high-frequency electron spin resonance (HF-ESR) measurements combined with Mossbauer spectroscopy and density-functional calculations. We show that this compound develops ferrimagnetic order below T-C = 9.5K and reveals a magnetization plateau at 1/3 saturation. The plateau extends to B-c similar to 8T, whereas above B-c the magnetization increases linearly until reaching saturation at B-s similar to 27 T. The Mossbauer spectroscopy reveals two magnetically nonequivalent iron sites with the 2: 1 ratio. The HF-ESR spectra are consistent with a two-sublattice ferrimagnet and additionally pinpoint weak magnetic anisotropy as well as short-range spin order that persists well above T-C. The ferrimagnetic order in the title compound is stabilized by a network of purely antiferromagnetic exchange interactions. The spin lattice comprises layers coinciding with the crystallographic (10-1) planes, with stronger couplings J(i) similar to 1.5 K within the layers and weaker couplings J(i) = 0.3-0.4K between the layers. Both intralayer and interlayer couplings are frustrated. The ensuing ferrimagnetic order arises from a subtle interplay of the frustrated but nonequivalent exchange couplings.