Absolute density measurements of low-ionization-degree or low-density plasmas ionized by lasers are very important for understanding strong-field physics, atmospheric propagation of intense laser pulses, Lidar etc. A cross-polarized common-path temporal interferometer using balanced detection was developed for measuring plasma density with a sensitivity of ∼0.6 mrad, equivalent to a plasma density-length product of ∼2.6 × 1013 cm-2 if using an 800 nm probe laser. By using this interferometer, we have investigated strong-field ionization yield versus intensity for various noble gases (Ar, Kr, and Xe) using 800 nm, 55 fs laser pulses with both linear (LP) and circular (CP) polarization. The experimental results were compared to the theoretical models of Ammosov-Delone-Krainov (ADK) and Perelomov-Popov-Terent'ev (PPT). We find that the measured phase change induced by plasma formation can be explained by the ADK theory in the adiabatic tunneling ionization regime, while PPT model can be applied to all different regimes. We have also measured the photoionization and fractional photodissociation of molecular (MO) hydrogen. By comparing our experimental results with PPT and MO-PPT models, we have determined the likely ionization pathways when using three different pump laser wavelengths of 800 nm, 400 nm, and 267 nm.