Chemical waves propagate in thin gel layers saturated with Belousov-Zhabotinsky (BZ) reaction solution. When a layer is in contact with air, weakly interacting waves can propagate along the top and the bottom of the layer. Experiments on the ferrion-catalyzed BZ reaction with stepwise layers reveal a poorly excitable sublayer in the middle of the layer. We propose that in a BZ excitable layer open to air two opposite transverse concentration gradients are established, those of oxygen and bromine. The bromine gradient results in a parallel gradient of the total concentration of bromo derivatives of malonic acid (BrMAs). The threshold of excitability increases with the concentrations of oxygen and of BrMAs. As a result, the excitability threshold varies nonmonotonically, with a maximum in the middle of the layer. If this maximum of the excitability threshold is high enough, a poorly excitable sublayer appears between the two excitable sublayers at the top and bottom. The wave propagation and interaction have been simulated using an Oregonator-type model with a nonmonotonic vertical profile of the stoichiometric factor q that relates Br- production to ferriin reduction. The simulation confirms that the observed stratification of layers can be explained by the established mechanism of the BZ reaction supplemented with molecular diffusion.