X-ray/optical cross-correlation methods are attracting increasing interest for exploring transient states of matter using ultrashort free-electron laser (FEL) pulses. Our paper shows that in such studies the difference in the penetration depth of the FEL-pump and the infrared (IR) probe pulses become important, in particular, when exploring the changes in the optical properties of solid targets. We discuss the role of interference effects, using a phenomenological model with excited and unperturbed slabs. The reliability of this model was experimentally verified by measuring the transient optical response of free-standing and silicon (Si) supported silicon nitride (Si3N4) films, simultaneously in reflection and transmission, using s- and p-polarized IR light. The changes in the Si3N4 optical refractive index, induced by the FEL pulses, have fully been described in the frame of the proposed model. The experimental results confirm that the differences, observed in the FEL-induced transient reflectance and transmittance of the Si3N4 targets with different thicknesses, arise from multilayer-like interferometric phenomena.
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