We present the second part of an H-band (1.6 microns) atlas of z<0.3 3CR radio galaxies, using the Hubble Space Telescope Near Infrared Camera and Multi-Object Spectrometer (HST NICMOS2). We present new imaging for 21 recently acquired sources, and host galaxy modeling for the full sample of 101 (including 11 archival) -- an 87% completion rate. Two different modeling techniques are applied, following those adopted by the galaxy morphology and the quasar host galaxy communities. Results are compared, and found to be in excellent agreement, although the former breaks down in the case of strongly nucleated sources. Companion sources are tabulated, and the presence of mergers, tidal features, dust disks and jets are catalogued. The tables form a catalogue for those interested in the structural and morphological dust-free host galaxy properties of the 3CR sample, and for comparison with morphological studies of quiescent galaxies and quasar host galaxies. Host galaxy masses are estimated, and found to typically lie at around 2*10^11 solar masses. In general, the population is found to be consistent with the local population of quiescent elliptical galaxies, but with a longer tail to low Sersic index, mainly consisting of low-redshift (z<0.1) and low-radio-power (FR I) sources. A few unusually disky FR II host galaxies are picked out for further discussion. Nearby external sources are identified in the majority of our images, many of which we argue are likely to be companion galaxies or merger remnants. The reduced NICMOS data are now publicly available from our website (http://archive.stsci.edu/prepds/3cr/)