We probe the interface between a phase-separated Bose-Fermi mixture consisting of a small Bose-Einstein condensate of ^{41}K residing in a large Fermi sea of ^{6}Li. We quantify the residual spatial overlap between the two components by measuring three-body recombination losses for variable strength of the interspecies repulsion. A comparison with a numerical mean-field model highlights the importance of the kinetic energy term for the condensed bosons in maintaining the thin interface far into the phase-separated regime. Our results demonstrate a corresponding smoothing of the phase transition in a system of finite size.