Self-assembled two-phase heterostructures of BiFeO3 and CuFe2O4 (BFO-CuFO) were deposited on (100)-oriented SrRuO3-buffered Pb(Mg1/3Nb2/3) O-3-33at%PbTiO3 (PMN-PT) by using switching pulsed laser deposition (SPLD), and compared to single layers of CuFO on the same single crystal substrate. The CuFO phase of the self-assembled layers had notably slimmer M-H loops than for previously reported vertically integrated CoFe2O4 nanopillar ones, but wider ones than for CuFO/PMN-PT heterostructures. Notable changes in the magnetization of the CuFO nanopillars were found with applied DC electric field (E-DC), where M-r/M-s exhibited typical butterfly-shaped hysteresis with E-DC. This was in distinct difference to CuFO/PMN-PT heterostructures which did not exhibit magnetoelectric coupling. The findings demonstrate a trade-off between magnetoelectric/magnetostrictive properties and loss that can be controlled by nanostructure features.