Understanding the penetration of liquids within textile fibers is critical for the development of next-generation smart textiles. Despite substantial research on liquid penetration in the plane of textile, little is known about how the liquid penetrates in the thickness direction. Here we report a time-resolved high-resolution X-ray measurement of the motion of the liquid-air interface within a single layer textile, as the liquid is transported across the textile thickness following the deposition of a droplet. The measurement of the time-dependent position of the liquid meniscus is made possible by the use of ultra-high viscosity liquids (dynamic viscosity from 10(5) to 2.5 x 10(6) larger than that of water). This approach enables imaging due to the slow penetration kinetics. Imaging results suggest a three-stage penetration process with each stage being associated with one of the three types of capillary channels existing in the textile geometry, providing insights into the effect of the textile structure on the path of the three-dimensional liquid meniscus. One dimensional kinetics studies show that our data for the transverse penetration depth Delta x(L) vs. time do not conform to a power law, and that the measured rate of penetration for long times is smaller than that predicted by Lucas-Washburn kinetics, challenging commonly held assumptions regarding the validity of power laws when applied to relatively thin textiles.