We present an approach to monitor the parity of wave functions of electronic states of bulk solids, which was elaborated on the model Ag) W(110) system. The dispersion of quantum- well (QW) states formed in the thin Ag layer was examined by means of angle-resolved photoemission. The obtained experimental data were compared with results of layer Korringa -Kohn -Rostoker calculations. We found that around k points, where the two-dimensional QW bands cross the projected bulk bands of the W substrate of the same symmetry, broad hybridization gaps in the QW distributions are observed. Careful analysis based on a symmetry approach for the electronic bands in the Ag monolayer and the W substrate suggests that respective gaps may generally be taken as a fingerprint for the interaction with substrate states of even parity with respect to the emission plane. We anticipate that QW states may be used as a probe for symmetry properties of strongly correlated states in systems like heavy-fermion compounds that are difficult to access theoretically within an ab initio approach.