A heterostructured cladding solid-core photonic bandgap fiber (HCSC-PBGF) is designed and fabricated which supports strong core mode and cladding mode transmission in a wide bandgap. An in-line Mach-Zehnder interferometer (MZI) curvature sensor is constructed by splicing single mode fibers at both ends of a HCSC-PBGF. Theoretical analysis of this heterostructured cladding design has been implemented, and the simulation results are consistent with experiment results. Benefiting from the heterostructured cladding design, an enhanced curvature sensing sensitivity of 24.3 nm/m-1 in the range of 0-1.75 m-1 and a high quality interference spectrum with 20 dB fringe visibility are achieved. In order to eliminate the interference of longitudinal strain and transverse torsion on the result of the curvature sensing experiment, we measure the longitudinal strain and transverse torsion sensing properties of HCSC-PBGF, and the results show that the impact is negligible. It is obvious that this high-sensitivity and cost-effective all fiber sensor with a compact structure will have a promising application in fiber sensing.