We have analyzed a brief period of same-day observations of the Martian ionosphere using data obtained in December 2004 from the Mars Global Surveyor (MGS) and Mars Express (MEX) radio occultation experiments. Such two-satellite, dual-hemisphere data sets are unique for the modern era of ionospheric observations at Mars and provide good test cases for constraints of key parameters commonly used in models of the Martian ionosphere. Several iterations of a 1-dimensional model are developed in attempts to simulate more successfully the altitudes, absolute magnitudes and shapes of the two photo-chemical layers (M1 and M2) obtained during the joint MGS-MEX observing period. The occurrence of same day, separate hemisphere, radio occultation profiles is important because the solar irradiance has to be held constant for modeling both sites, and thus this is the first study of this kind to be done. The overall results stress the dominant influence of solar zenith angle effects on production for the M2-layer via primary solar ionization, its augmentation by 30% due to secondary ionization, and further enhancements due to reduced chemical loss when the electron temperature exceeds the neutral temperature. Secondary ionization is the most crucial process for the M1-layer.