Recent pump-probe experiments reported an enhancement of superconducting transport along the c axis of underdoped YBa2Cu3O6+delta (YBCO), induced by a midinfrared optical pump pulse tuned to a specific lattice vibration. To understand this transient nonequilibrium state, we develop a pump-probe formalism for a stack of Josephson junctions, and we consider the tunneling strengths in the presence of modulation with an ultrashort optical pulse. We demonstrate that a transient enhancement of the Josephson coupling can be obtained for pulsed excitation and that this can be even larger than in a continuously driven steady state. Especially interesting is the conclusion that the effect is largest when the material is parametrically driven at a frequency immediately above the plasma frequency, in agreement with what is found experimentally. For bilayer Josephson junctions, an enhancement similar to that experimentally is predicted below the critical temperature T-c. This model reproduces the essential features of the enhancement measured below T-c. To reproduce the experimental results above T-c, we will explore extensions of this model, such as in-plane and amplitude fluctuations, elsewhere.