The possibility to develop neuromorphic computing devices able to mimic the extraordinary data processing capabilities of biological systems spurs the research on memristive systems. Memristors with additional functionalities such as robust memcapacitance can outperform standard devices in key aspects such as power consumption or miniaturization possibilities. In this work, we demonstrate a large memcapacitive response of a perovskite memristive interface, using the topotactic redox ability of La$_{0.5}$Sr$_{0.5}$Mn$_{0.5}$Co$_{0.5}$O$_{3-delta}$ (LSMCO, 0 $leq$ $delta$ $leq$ 0.62). We demonstrate that the multi-mem behaviour originates at the switchable n-p diode formed at the Nb:SrTiO3/LSMCO interface. We found for our Nb:SrTiO$_{3}$/LSMCO/Pt devices a memcapacitive effect C$_{HIGH}$/C$_{LOW}$ ~ 100 at 150 kHz. The proof-of-concept interface reported here opens a promising venue to use topotactic redox materials for disruptive nanoelectronics, with straightforward applications in neuromorphic computing technology.