Cold plasma mass density profiles in the plasmasphere have been determined for the geomagnetically quiet day of 19th August 2000 using the cross-phase technique applied to ground-based magnetometer data from the SAMNET, IMAGE and BGS magnetometer arrays. Cross-phase derived mass densities have been compared to electron densities derived from both ground-based VLF receiver measurements, and the IMAGE satellite RPI. The cross-phase results are in excellent agreement with both the VLF and IMAGE observational results, thus validating the cross-phase technique during quiet times. This is the first such coordinated multi-instrument study, and has enabled very few heavy ions to be inferred in the plasmasphere for L > 3.45 on this day. The observational results were compared to plasma mass densities from the SUPIM model and were found to be in excellent agreement. IMAGE EUV data also verified the existence of azimuthal structure in the outer quiet-time plasmasphere.