We consider two-species random sequential adsorption (RSA) in which species A and B adsorb randomly on a lattice with the restriction that opposite species cannot occupy nearest-neighbor sites. When the probability x_{A} of choosing an A particle for an adsorption trial reaches a critical value 0.626441(1), the A species percolates and/or the blocked sites X (those with at least one A and one B nearest neighbor) percolate. Analysis of the size-distribution exponent τ, the wrapping probabilities, and the excess cluster number shows that the percolation transition is consistent with that of ordinary percolation. We obtain an exact result for the low x_{B}=1-x_{A} jamming behavior: θ_{A}=1-x_{B}+b_{2}x_{B}^{2}+O(x_{B}^{3}), θ_{B}=x_{B}/(z+1)+O(x_{B}^{2}) for a z-coordinated lattice, where θ_{A} and θ_{B} are, respectively, the saturation coverages of species A and B. We also show how differences between wrapping probabilities of A and X clusters, as well as differences in the number of A and X clusters, can be used to find the percolation transition point accurately.