We announce the initial release of data from the Ohio State University (OSU) Bright Spiral Galaxy Survey, a BVRJHK imaging survey of a well-defined sample of 205 bright, nearby spiral galaxies. We present H-band morphological classification on the Hubble sequence for the OSU Survey sample. We compare the H-band classification to B-band classification from our own images and from standard galaxy catalogs. Our B-band classifications match well with those of the standard catalogs. On average, galaxies with optical classifications from Sa through Scd appear about one T type earlier in the H band than in the B band, but with large scatter. This result does not support recent claims made in the literature that the optical and near-IR morphologies of spiral galaxies are uncorrelated. We present detailed descriptions of the H-band morphologies of our entire sample, as well as B- and H-band images for a set of 17 galaxies chosen as type examples and BRH color-composite images of six galaxies chosen to demonstrate the range in morphological variation as a function of wavelength.