Quantitative morphological and structural parameters are estimated for galaxies detected in Hubble Space Telescope observations of WFPC2 survey fields. A modeling approach based on maximum likelihood has been developed for two-dimensional decomposition of faint undersampled galaxy images into components of disk and bulge morphology. Decomposition can be achieved for images down to F814W (I) approximate to 23.0, F606W (V) approximate to 23.8, and F450W (B) approximate to 23.3 mag in WFPC2 exposures of 1 hr. We discuss details of the fitting procedure and present the observed distributions of magnitude, color, effective half-light radius, disk and bulge axis ratios, bulge-to-(disk + bulge) flux ratio, bulge-to-disk half-light radius ratio, and surface brightness. We also discuss the various selection limits on the measured parameters. The Medium Deep Survey catalogs and images of random pure parallel fields and other similar archival primary WFPC2 fields have been made available via the Internet with a searchable browser interface to the database.