Microwave photonic bandpass filters (MPBPFs) are important building blocks in radio-frequency (RF) signal processing systems. However, most of the reported MPBPFs fail to satisfy the stringent real-world performance metrics, particularly low RF insertion loss. In this paper we report a novel MPBPF scheme using two cascaded integrated silicon nitride (Si3N4) ring resonators, achieving a high link gain in the RF filter passband. In this scheme, one ring operates at an optimal over-coupling condition to enable a strong RF passband whilst an auxiliary ring is used to increase the detected RF signal power via tuning the optical carrier-to-sideband ratio. The unique combination of these two techniques enables compact size as well as high RF performance. Compared to previously reported ring-based MPBPFs, this work achieves a record-high RF gain of 1.8 dB in the passband, with a high spectral resolution of 260 MHz. Furthermore, a multi-band MPBPF with optimized RF gain, tunable central frequencies, and frequency spacing tunability is realized using additional ring resonators, highlighting the scalability and flexibility of this chip-based MPBPF scheme.