An asymmetric tubular carbon membrane, appropriate for gas separation applications, was made through carbonization at 800 degrees C of a precursor structure containing two phenol-formaldehyde resins, a partially cured novolac resin in 30-60 mu m grains (bulk material), and a resole resin (membrane, skin material). A replica of the skin material was deposited separately on a stainless steel substrate. The samples were analyzed by nitrogen adsorption, small-angle neutron scattering, and scanning electron microscopy (SEM). The basic structural entities of both skin and the bulk part were low-aspect-ratio carbon domains with a characteristic dimension in the 4.0-4.5 nm range. Further, the materials were characterized by microporosity in the 0.30-0.50 range with isotropic pores having a 1.3 nm diameter. The results are discussed with the help of a systematic survey of possible carbon structures with an intermediate level of microporosity.