We introduce an extended transfer matrix method (TMM) for solving guided modes in leaky optical fibers with layered cladding. The method can deal with fibers with circular but nonconcentric material interfaces. Validity of the method is verified by two full-vector numerical methods. The TMM is then used to investigate the guidance property of perturbed Bragg fibers. Our analysis reveals that the core modes will interact with each other when a perturbed Bragg fiber has only C(1) symmetry. Special attention is paid to the first transverse-electric (TE(01)) mode, which is found to experience severe degradation around spectral regions where its dispersion curve supposedly crosses a transverse-magnetic (TM) or hybrid mode.