By means of extensive Monte Carlo simulations of the bond fluctuation model, we study the effect of adding AB diblock copolymers on the properties of an interface between demixed homopolymer phases. The parameters are chosen such that the homopolymers are strongly segregated, and the whole range of copolymer concentrations in the two phase coexistence region is scanned. We compare the "mushroom＇＇ regime, in which copolymers are diluted and do not interact with each other, with the "wet brush＇＇ regime, where copolymers overlap and stretch, but are still swollen by the homopolymers. A "dry brush＇＇ regime is never entered for our choice of chain lengths. "Intrinsic＇＇ profiles are calculated using a block analysis method introduced by us in earlier work. We discuss density profiles, orientational profiles, and contact number profiles. In general, the features of the profiles are similar at all copolymer concentrations, however, the profiles in the concentrated regime are much broader than in the dilute regime. The results compare well with self-consistent field calculations.