We present optical and near-infrared (NIR, Y-, J-, H-band) observations of 42 Type Ia supernovae (SNe Ia) discovered by the untargeted intermediate Palomar Transient Factory survey. This new data set covers a broad range of redshifts and host galaxy stellar masses, compared to previous SN Ia efforts in the NIR. We construct a sample, using also literature data at optical and NIR wavelengths, to examine claimed correlations between the host stellar masses and the Hubble diagram residuals. The SN magnitudes are corrected for host galaxy extinction using either a global total-to-selective extinction ratio, R_V = 2.0, for all SNe, or a best-fit R_V for each SN individually. Unlike previous studies that were based on a narrower range in host stellar mass, we do not find evidence for a "mass step," between the color- and stretch-corrected peak J and H magnitudes for galaxies below and above . However, the mass step remains significant (3σ) at optical wavelengths (g, r, i) when using a global R_V, but vanishes when each SN is corrected using their individual best-fit R_V. Our study confirms the benefits of the NIR SN Ia distance estimates, as these are largely exempted from the empirical corrections dominating the systematic uncertainties in the optical.