We analyze more than 5000 days of high-quality Sun-as-a-star, radial velocity GOLF and photometric VIRGO/SPM helioseismic observations to extract precise estimates of the visibilities of the low-degree p modes and the m-height ratios of the l = 2 and 3 multiplets in the solar acoustic spectrum. The mode visibilities are shown to be larger during the GOLF red-wing configuration than during the blue-wing configuration, and to decrease as the wavelength of the VIRGO/SPM channels increases. We also show that the mode visibilities are independent of the solar activity cycle and remain constant overall with time, but that nevertheless they follow short-term fluctuations on a time scale of a few months. The l = 1 mode visibility also increases significantly toward the end of the year 1999. Comparisons with theoretical predictions are provided. Even though there is qualitative agreement, some significant discrepancies appear, especially for the l = 3 modes. The limb darkening alone cannot explain the relative visibilities of modes. These precise estimates should be used as references for the extraction of the p-mode parameters for any future investigation using the GOLF and VIRGO/SPM observations. Appendices A and B are only available in electronic form at http://www.aanda.org