We present the first measurements of the thermal boundary resistance of the interface between the two different liquid phases: bulk superfluid and liquid confined in aerogel. We set up a heat flow along a liquid-filled tube containing a plug of 98% aerogel, and measure the temperature at the two ends. At the lowest temperatures, the resistance is dominated by the boundary resistance at the aerogel surfaces and is unaffected by the superfluid transition of the He-3 in the aerogel. Whereas in conventional Kapitza resistance the boundary conductance is limited by acoustic mismatch, here the conductance is limited by an energy mismatch, since quasiparticles with energies above the bulk B-phase gap may freely cross the interface, while those with lower energies are confined to the aerogel.