  We consider the Feigin-Fuchs-Felder formalism of the $SU(2)_k\times
SU(2)_l/SU(2)_{k+l}$ coset minimal conformal field theory and extend it to
higher genus. We investigate a double BRST complex with respect to two
compatible BRST charges, one associated with the parafermion sector and the
other associated with the minimal sector in the theory. The usual screened
vertex operator is extended to the BRST invariant screened three string vertex.
We carry out a sewing operation of these string vertices and derive the BRST
invariant screened $g$-loop operator. The latter operator characterizes the
higher genus structure of the theory. An analogous operator formalism for the
topological minimal model is obtained as the limit $ l=0$ of the coset theory.
We give some calculations of correlation functions on higher genus.
