Algorithms for estimating the percolation probabilities and cluster size distribution are given in the framework of a Monte Carlo simulation for disordered lattices for the generalized site-bond problem. The site-bond approach is useful when a percolation process cannot be exclusively described in the context of pure site or pure bond percolation. An extended multiple labeling technique (ECMLT) is introduced for the generalized problem. The ECMLT is applied to the site-bond percolation problem for square and triangular lattices. Numerical data are given for lattices containing up to 16 million sites. An application to polymer gelation is suggested.