The dispersion interaction between two pointlike particles confined in a dielectric slab between two plates of another dielectric medium is studied within a continuum (Lifshitz) theory. The retarded (Casimir-Polder) interaction at large interparticle distances is found to be strongly enhanced as the mismatch between the dielectric permittivities of the two media is increased. The large-distance interaction is multiplied due to confinement by a factor of (33gamma(5/2) + 13gamma(-3/2))/46 at zero temperature, and by (5gamma2 + gamma(-2))/6 at finite temperature, gamma = epsilon(in)(0)/epsilon(out)(0) being the ratio between the static dielectric permittivities of the inner and outer media. This confinement-induced amplification of the dispersion interaction can reach several orders of magnitude.