Frontal photopolymerization (FPP) offers numerous advantages for the rapid prototyping of microfluidic devices. Quantitative utilization of this method, however, requires a control of the vertical dimensions of the patterned resist material. To address this fundamental problem, we study the ultraviolet (UV) photopolymerization of a series of multifunctional thiolene resists through a combination of experiments and analytical modeling of the polymerization fronts. We describe this nonlinear spatio-temporal growth process in terms of a "minimal" model involving an order parameter phi(x, t) characterizing the extent of monomer-to-polymer conversion, the optical attenuation T(x, t), and the solid front position h(t). The latter exhibits an induction time (or equivalent critical UV dose) characterizing the onset of frontal propagation. We also observe a novel transition between two logarithmic rates of growth, determined by the Beer-Lambert attenuation constants mu(0) and mu(infinity) of the monomer and fully polymerized material, respectively. The measured frontal kinetics and optical transmission of the thiolene resist materials are consistent with our photopolymerization model, exhibiting both "photodarkening" and "photoinvariant" polymerization. This is apparently the first observation of photodarkening reported in FPP. On the basis of these results, multilevel fluidic devices with controlled height are readily fabricated with modulated illumination. A representative two-level microfluidic device, incorporating a chaotic mixer, a T junction, and a series of controlled flow constrictions, illustrates the practical versatility of this fabrication method.