We report on a statistical study of 51 radio galaxies at the millijansky flux level selected from the Faint Images of the Radio Sky at Twenty cm survey, including their optical morphologies and structure obtained with the Hubble Space Telescope (HST). Our optical imaging is significantly deeper (~2mag) than previous studies with the superior angular resolution of space-based imaging. We that find 8/51 (16%) of the radio sources have no optically identifiable counterpart to AB~24mag. For the remaining 43 sources, only 25 are sufficiently resolved in the HST images to reliably assign a visual classification: 15 (60%) are elliptical galaxies, two (8%) are late-type spiral galaxies, one (4%) is an S0, three (12%) are pointlike objects (quasars), and four (16%) are merger systems. We find a similar distribution of optical types with measurements of the Sersic index.