We report a combined experimental and theoretical investigation of electron–molecule interactions using pyrrole as a model system. Experimental two-dimensional electron energy loss spectra (EELS) encode information about the vibrational states of the molecule as well as the position and structure of electronic resonances. The calculations using complex-valued extensions of equation-of-motion coupled-cluster theory (based on non-Hermitian quantum mechanics) facilitate the assignment of all major EELS features. We confirm the two previously described π resonances at about 2.5 and 3.5 eV (the calculations place these two states at 2.92 and 3.53 eV vertically and 2.63 and 3.27 eV adiabatically). The calculations also predict a low-lying resonance at 0.46 eV, which has a mixed character—of a dipole-bound state and σ* type. This resonance becomes stabilized at one quanta of the NH excitation, giving rise to the sharp feature at 0.9 eV in the corresponding EELS. Calculations of Franck–Condon factors explain the observed variations in the vibrational excitation patterns. The ability of theory to describe EELS provides a concrete illustration of the utility of non-Hermitian quantum chemistry, which extends such important concepts as potential energy surfaces and molecular orbitals to states embedded in the continuum.