Pulsed electromagnetic (EM) plane-wave interaction with time-varying (TV) highly-contrasting thin sheets are analyzed analytically in the time domain (TD). With the aid of a rigorous analytical procedure, closed-form TD analytical expressions are derived for both E- and H-polarized TD reflection and transmission coefficients. The coefficients are subsequently used to express TD EM fields in the presence of a thin layer with TV conductive and dielectric properties. Illustrative examples concerning selected types of the temporal modulation function are discussed and numerically evaluated.