A mean-field theory is presented to describe the surface tension and interfacial profile of compositionally homogeneous, random A-B multiblock copolymer melts in contact with air or a solid substrate. The copolymer model accounts for variations in average composition and block sequence distribution and reduces to a model for a statistical copolymers as the block size approaches that of a monomer. It is found that, to prevent unphysical behavior of the surface tension and profile, one must explicitly incorporate into the theory the effect of the surface on the chain conformations. This is done by deriving an expression for the free energy of a random copolymer melt in contact with a neutral impenetrable surface. With this free energy we find that, depending upon the type of chemical correlations between successive segments and the temperature, the composition profile can either be oscillatory or monotonic. Further, "blocky" copolymers with a tendency for repeated segments of A or B are predicted to have a lower surface tension than copolymers with a tendency for alternation of A and B segments.