We present constraints on models containing non-standard model values for the spin J and parity P of the Higgs boson, H, in up to 9.7 fb −1 of pp collisions at √ s = 1.96 TeV collected with the D0 detector at the Fermilab Tevatron Collider. These are the first studies of Higgs boson J P with fermions in the final state. In the ZH → ℓℓb b, W H → ℓνb b, and ZH → ννb b final states, we compare the standard model (SM) Higgs boson prediction, J P = 0 + , with two alternative hypotheses, J P = 0 − and J P = 2 + . We use a likelihood ratio to quantify the degree to which our data are incompatible with non-SM J P predictions for a range of possible production rates. Assuming that the production rate in the signal models considered is equal to the SM prediction, we reject the J P = 0 − and J P = 2 + hypotheses at the 97.6% CL and at the 99.0% CL, respectively. The expected exclusion sensitivity for a J P = 0 − (J P = 2 + ) state is at the 99.86% (99.94%) CL. Under the hypothesis that our data is the result of a combination of the SM-like Higgs boson and either a J P = 0 − or a J P = 2 + signal, we exclude a J P = 0 − fraction above 0.80 and a J P = 2 + fraction above 0.67 at the 95% CL. The expected exclusion covers J P = 0 − (J P = 2 + ) fractions above 0.54 (0.47).