The Kazama-Suzuki coset vertex operator superalgebra associated with a simple Lie algebra g and its Cartan subalgebra h is a ``super-analog'' of the parafermion vertex operator algebra associated with g. At positive integer levels, the coset superalgebra turns out to be C_2-cofinite and rational by the general theory of orbifolds (Miyamoto) and Heisenberg cosets (Creutzig-Kanade-Linshaw-Ridout), respectively. On the other hand, at Kac-Wakimoto admissible levels, the coset superalgebra is not C_2-cofinite nor rational. In this talk we discuss a relationship between the category of weight modules for the admissible affine vertex algebra associated with g and that for the corresponding Kazama-Suzuki coset vertex superalgebra. In our discussion the inverse Kazama-Suzuki coset construction, which is originally due to Feigin-Semikhatov-Tipunin in the g=sl_2 case, plays an important role. As an application, for g=sl_2 at level -1/2, we determine all the fusion rules between simple weight modules of the Kazama-Suzuki coset vertex superalgebra and verify the conjectural Verlinde formula in this case (corresponding to Creutzig-Ridout's result in the affine side). The last part is based on the joint work with Shinji Koshida.