A stellar-mass binary black hole (BBH) may merge efficiently in the vicinity of a supermassive black hole (SMBH). Moreover, such a BBH will stay in the sensitivity band of a space-borne gravitational-wave (GW) detector for years. We can then use the BBH's GW emission as a signal carrier. By searching for modulations induced by the SMBH on the carrier, we can thus probe the properties of the SMBH. This method can be applied to SMBHs at cosmological distances and it works independent of the SMBH being active or quiescent.