The ground state rotational spectra and internal dynamics in five isotopomers N-14(2)-IH, N-14(2)-ID, N-15(2)-IH, (NN)-N-14-N-15-IH, and (NN)-N-15-N-14-IH of the nitrogen-hydrogen iodine dimer have been investigated by pulsed-nozzle, Fourier-transform microwave spectroscopy. Analysis of the recorded spectra yields rotational, centrifugal distortion, nuclear quadrupole and spin-rotation coupling constants for the five isotopomers. The spectroscopic constants are interpreted in terms of a ground-state NN-IH structure using the parameters r(cm), k(sigma), and the oscillation angles theta(N2) and theta(HI) of the N-2 and IH moieties. For N-14(2)-IH, the values r(cm)=4.197 872(67) Angstrom, k(sigma)=1.461 52(32) N/m, theta(N2)=25.61(22)degrees, and theta(HI)=23.454 6(91)degrees are obtained. The rotational transitions of N-14(2)-IH, N-14(2)-ID, and N-15(2)-IH show a doubling, which is a consequence of tunneling associated with the interchange of the two nitrogen nuclei. The experimental findings are compared with results from ab initio calculations.