An analytic approach to the theory of the optical defect modes in chiral liquid crystals (CLC) for the case of a birefringent defect layer is developed. The analytic study is facilitated by the choice of the problem parameters. Namely, a birefringent layer (with the averaged dielectric susceptibility equal to the average dielectric susceptibility of CLC) sandwiched between two CLC layers inserted in an isotropic medium with the dielectric constant equal to the average dielectric constant of CLC is studied. The chosen model allows one to get rid off the polarization mixing at the external surfaces of the defect structure (DMS) and to reduce the corresponding equations to the equations for light of diffracting in CLC polarization only. The dispersion equation determining connection of the defect mode frequency with the layer birefringence and other parameters of the defect structure is obtained. Analytic expressions for the transmission and reflection coefficients of the defect mode structure (CLC-birefringent defect layer-CLC) are presented and analyzed. It is shown that generally speaking the layer birefringence reduces the DM lifetime in comparison with the DMS with an isotropic defect layer and only at discrete values of DMS parameters it achieves the value of the corresponding DMS with an isotropic defect layer. Correspondingly, generally speaking, the effect of anomalously strong light absorption at the defect mode frequency and the lowering of the lasing threshold are not so pronounced as in the case of the DMS with an isotropic defect layer. The case of DMS with low defect layer birefringence is studied in details. The options of effectively influence at the DM parameters by changing the defect layer birefringence are discussed.