Lithium niobate on insulator (LNOI) has been demonstrated as a promising platform for photonic integrated circuits (PICs), thanks to its excellent properties such as strong electro-optic effect, low material loss and wide transparency window. In this paper, we propose and demonstrate a monolithic PIC for high-speed data communication application on a lithium-niobate-etchless platform with silicon nitride (Si3N4) as a loading material. The fabricated PIC consists of four racetrack resonator modulators and a pair of four-channel mode (de)multiplexers, which shows high data modulation rate of 70 Gbps for single channel and the total data throughput reaches up to 280 Gbps. To the best of our knowledge, this is the first demonstration of PIC consisting of high-speed electro-optical modulators and (de)multiplexers with such high data capacity on Si3N4-LNOI hybrid platform, which opens up new avenues for achieving large-scale monolithic integration on LNOI platform in future.