We analyze 143 Type Ia supernovae (SNe Ia) observed in H band (1.6-1.8{mu}m) and find that SNe Ia are intrinsically brighter in H band with increasing host galaxy stellar mass. We find that SNeIa in galaxies more massive than 10^10.43^M_{sun}_ are 0.13+/-0.04mag brighter in H than SNe Ia in less massive galaxies. The same set of SNe Ia observed at optical wavelengths, after width-color-luminosity corrections, exhibit a 0.10+/-0.03mag offset in the Hubble residuals. We observe an outlier population (|{Delta}H_max_|>0.5mag) in the H band and show that removing the outlier population moves the mass threshold to 10^10.65^M_{sun}_ and reduces the step in H band to 0.08+/-0.04mag, but the equivalent optical mass step is increased to 0.13+/-0.04mag. We conclude that the outliers do not drive the brightness-host-mass correlation. Less massive galaxies preferentially host more higher-stretch SNe Ia, which are intrinsically brighter and bluer. It is only after correction for width-luminosity and color-luminosity relationships that SNe Ia have brighter optical Hubble residuals in more massive galaxies. Thus, finding that SNe Ia are intrinsically brighter in H in more massive galaxies is an opposite correlation to the intrinsic (pre-width-luminosity correction) optical brightness. If dust and the treatment of intrinsic color variation were the main driver of the host galaxy mass correlation, we would not expect a correlation of brighter H-band SNeIa in more massive galaxies.