Flux-line confinement by triangular and square regular arrays of microholes (''antidots'') has been studied in superconducting films (Pb, WGe) and multilayers (Pb/Ge). For relatively large antidots sharp cusp-like magnetization anomalies appear at the matching fields Hm. These anomalies are caused by the formation of the multi-quanta vortex lattices at each subsequent Hm. The multi-quanta vortex lattices make possible a peacefull coexistence of the flux penetration at the antidots and the presence of a substantial superfluid density in the space between them. This leads to a very strong enhancement of the critical current density in films with an antidot lattice. For smaller antidots the vortices are forced to occupy the interstitial positions after the saturation of the pinning sites at antidots. This leads to the formation of the novel composite flux-line lattices consisting from the interpenetrating sublattices of weakly pinned interstitial single-quantum vortices and multi-quanta vortices strongly pinned by the antidots. When the interstitial flux-line lattice melts, it forms the interstitial flux liquid coexisting with the flux solid at antidots.