In this work we study theoretically and experimentally the multi-particle structure of the so-called type-II quantum dots with spatially separated electrons and holes. Our calculations based on customarily developed full configuration interaction ap- proach reveal that exciton complexes containing holes interacting with two or more electrons exhibit fairly large antibinding energies. This effect is found to be the hallmark of the type-II confinement. In addition, an approximate self-consistent solution of the multi-exciton problem allows us to explain two pronounced phenomena: the blue-shift of the emission with pumping and the large inhomogeneous spectral broadening, both of those eluding explanation so far. The results are confirmed by detailed intensity and polarization resolved photoluminescence measurements on a number of type-II samples.