The behavior of both flexible and semiflexible polymers near a liquid-liquid interface is investigated with the aid of the self-consistent-field theory as developed by Scheutjens and Fleer. A ternary system (A/B-N/C) is studied near the wetting transition. In a symmetric system, i.e., chi(AB) = chi(BC) = chi, a change in the interaction parameter chi introduces a wetting transition. The ratio of the interfacial width xi of the binary A/C system and the coil size of the polymer determines the order of this transition. Beyond a certain chain length N-c (at fixed xi) the wetting transition is of first order, whereas it is of second order for N