Hybrid Photonic Crystal Fibers with a first ring of high index inclusions are studied and compared to both standard air-hole fibers and all solid photonic bandgap fibers. In such new fibers a bandgap-like core mode exists over a wide spectral range and exhibits confinement losses ten orders of magnitude smaller than those of the corresponding all-solid fiber. This particular fiber supports also a core mode guided by modified total internal reflection at long enough wavelengths. The origin and properties of these two kinds of modes are discussed in details. Such a design can also act as a mode filter (as compared to the standard air-hole structure) and could also be used to ease phase matching conditions for nonlinear optics.