Dust extinction can be determined from the number of distant field galaxies seen through a spiral disk. To calibrate this number for the crowding and confusion introduced by the foreground image, Gonzalez et al. and Holwerda et al. developed the Synthetic Field Method (SFM), which analyzes synthetic fields constructed by adding various deep exposures of unobstructed background fields to the candidate foreground galaxy field. The advantage of the SFM is that it gives the average opacity for the area of a galaxy disk without making assumptions about either the distribution of absorbers or of the disk starlight. However, it is limited by poor statistics on the surviving field galaxies, hence the need to combine a larger sample of fields. This paper presents the first results for a sample of 32 deep Hubble Space Telescope (HST)/WFPC2 archival fields of 29 spiral galaxies. The radial profiles of average dust extinction in spiral galaxies based on calibrated counts of distant field galaxies is presented here, both for individual galaxies and for composites from our sample. The effects of inclination, spiral arms, and Hubble type on the radial extinction profile are discussed. The dust opacity of the disk apparently arises from two distinct components: an optically thicker ( A(I) = 0.5-4 mag) but radially dependent component associated with the spiral arms and a relatively constant optically thinner disk ( A(I) = 0.5 mag). These results are in complete agreement with earlier work on occulted galaxies. The early-type spiral disks in our sample show less extinction than the later types. Low surface brightness galaxies, and possibly Sd's, appear effectively transparent. The average color of the field galaxies seen through foreground disks does not appear to change with radius or opacity. This gray behavior is most likely due to the patchy nature of opaque clouds. The average extinction of a radial annulus and its average surface brightness seem to correlate for the brighter regions. This leads to the conclusion that the brighter parts of the spiral disk, such as spiral arms, are also the ones with the most extinction associated with them.