Charged-hadron multiplicity distributions in n and p interactions are measured in an exposure of the Fermilab deuterium-filled 15-foot bubble chamber to a wide-band neutrino beam. Multiplicity moments are studied as functions of the invariant mass of the hadronic system W in the range 1<W<15 GeV. The mean multiplicities for both n and p are found to increase logarithmically with W2 with identical slopes but slightly different intercepts. A linear rise of the dispersion D with the mean multiplicity nch is observed with an approximate slope of 0.35. This value is similar to that found in e+e- and p»p annihilation and is much less than the asymptotic prediction of QCD. A close similarity between D- vs n- in n and p interactions is seen. Negative correlations between the multiplicity distributions in the forward and backward hadronic center-of-mass hemispheres are found and discussed.