We present isophotal profiles of six faint field galaxies from some of the first deep images taken for the Hubble Space Telescope (HST) Medium Deep Survey (MDS). These have redshifts in the range z = 0.126 to 0.402. The images were taken with the Wide Field Camera (WFC) in `parallel mode' and deconvolved with the Lucy method using as the point-spread function nearby stars in the image stack. The WFC deconvolutions have a dynamic range of 16 to 20 dB (4 to 5 mag) and an effective resolution approximately less than 0.2 sec (FWHM). The multiorbit HST images allow us to trace the morphology, light profiles, and color gradients of faint field galaxies down to V approximately equal to 22 to 23 mag at sub-kpc resolution, since the redshift range covered is z = 0.1 to 0.4. The goals of the MDS are to study the sub-kpc scale morphology, light profiles, and color gradients for a large samole of faint field galaxies down to V approximately equal to 23 mag, and to trace the fraction of early to late-type galaxies as function of cosmic time. In this paper we study the brighter MDS galaxies in the 13 hour + 43 deg MDS field in detail, and investigate to what extent model fits with pure exponential disks or a(exp 1/4) bulges are justified at V approximately less than 22 mag. Four of the six field galaxies have light profiles that indicate (small) inner bulges following r(exp 1/4) laws down to 0.2 sec resolution, plus a dominant surrounding exponential disk with little or no color gradients. Two occur in a group at z = 0.401, two are barred spiral galaxies at z = 0.179 and z = 0.302, and two are rather subluminous (and edge-on) disk galaxies at z = 0.126 and z = 0.179. Our deep MDS images can detect galaxies down to V, I approximately less than 25 to 26 mag, and demonstrate the impressive potential of HST--even with its pre-refurbished optics--to resolve morphological details in galaxies at cosmologically significant distances (v approximately less than 23 mag). Since the median redshift of these galaxies is approximately less than 0.4, the HST resolution allows us to study sub kpc size scales at the galaxy, which cannot be done with stable images over wide fields from the best ground-based sites.