We study the competitive irreversible adsorption of a binary mixture of monomers and square-shaped particles of linear size R on the square lattice. With the random sequential adsorption model, we investigate how the jamming coverage and percolation properties depend on the size ratio R and relative flux F. We find that the onset of percolation of monomers is always lower for the binary mixture than in the case with only monomers (R = 1). Moreover, for values F below a critical value, the higher is the flux or size of the largest species, the lower is the value of the percolation threshold for monomers.