Mastering the breakthrough process and predicting the breakthrough pressure in partially saturated porous media (PSPM) are crucial for evaluating the sealing ability of reservoir caprock to hydrocarbon, CO2, radiation, etc. An accurate model for predicting the breakthrough pressure in PSPM has not been put forward since the characteristic of the breakthrough point in PSPM is still mystified. In this paper, a microvisualization experimental system was set to capture gas-liquid displacement images in partially saturated glass planar pore networks (glass-PPNs) in real time. Breakthrough pressures and capillary pressures were measured by a step-by-step method. The measured capillary pressure curves (CPCs) were consistent with the van Genuchten model. The experimental results manifested that the inflection point of the CPC in PSPM characterizes the breakthrough point. Moreover, the effect of initial wetting phase saturation (IWPS) on breakthrough pressure was analyzed. The breakthrough pressure increases with the increasing IWPS at first. After achieving a specific level, IWPS exerts a weak influence on the breakthrough pressure, which is finally asymptotical to a maximum value. An asymptotic model was proposed to describe the law of breakthrough pressure with IWPS. Compared with the exponential model, the asymptotic model shows to be better consistent with other breakthrough pressure experiment results in partially saturated three-dimensional (3D) cores. Moreover, the theoretical expression of the asymptotic model when IWPS = 1 was derived based on the above inflection point theory and the porous media capillary bundle hypothesis.