A multiferroic interface between the antiferromagnetic Slater insulator SrTcO₃ and ferroelectric BaTiO₃ (BTO) is studied from first principles. Although the interfacial magnetoelectric coupling of SrTcO₃(001) is relatively small, we found that a two-dimensional electron gas (2DEG) appears for both BaO/TcO₂ and TiO₂/SrO terminations. The charge character of the carriers, induced in the band gap due to polar BTO, can be switched from electrons to holes by the reversal of the electric polarization in BTO. The 2DEG is robust and stable against the degree of electronic correlations, whereas the paraelectric state of BTO suppresses the 2DEG. The origin of the 2DEG at the BTO/SrTcO₃ interface and its key factors are discussed.