  We present a systematic approach to classify the three-level-like models with
two bound states coupled to a continuum. It is shown that, when one of the
discrete levels of usual three-level Lambda- ($\Lambda$), cascade ($\Xi$) or
Vee ($V$)-type systems is replaced by a continuum of states, the resulting each
model can be classified into three distinct categories with nine possible
configurations. We show that all these models are exactly solvable. We obtain
and compare the asymmetric Fano line shapes of the spectra for all the models.
Our results are important for exploring new coherent effects in a variety of
physical systems involving continuum-bound coupling such as photoassociation of
cold atoms, plasmonics, quantum dots, photonic crystals, electromagnetic
metamaterials and so on.
