We present data from the Supernova Cosmology Project for five high redshift Type Ia supernovae (SNe Ia) that were obtained using the NICMOS infrared camera on the Hubble Space Telescope. We add two SNe from this sample to a rest-frame I-band Hubble diagram, doubling the number of high redshift supernovae on this diagram. This I-band Hubble diagram is consistent with a flat universe (Omega_Matter, Omega_Lambda= 0.29, 0.71). A homogeneous distribution of large grain dust in the intergalactic medium (replenishing dust) is incompatible with the data and is excluded at the 5 sigma confidence level, if the SN host galaxy reddening is corrected assuming R_V=1.75. We use both optical and infrared observations to compare photometric properties of distant SNe Ia with those of nearby objects. We find generally good agreement with the expected color evolution for all SNe except the highest redshift SN in our sample (SN 1997ek at z=0.863) which shows a peculiar color behavior. We also present spectra obtained from ground based telescopes for type identification and determination of redshift.