Signal processing using on-chip nonlinear or linear optical effects has shown tremendous potential for RF photonic applications. Combining nonlinear and linear elements on the same photonic chip can further enable advanced functionality and enhanced system performance in a robust and compact form. However, the integration of nonlinear and linear optical signal processing units remains challenging due to the competing and demanding waveguide requirements, specifically the combination of high optical nonlinearity in single-pass waveguides, which is desirable for broadband signal processing with low linear loss and negligible nonlinear distortions required for linear signal processing. Here, we report the first demonstration of integrating Brillouin-active waveguides and passive ring resonators on the same integrated photonic chip, enabling an integrated microwave photonic notch filter with ultradeep stopband suppressions of >40 dB, a low filter passband loss of <-10 dB, flexible center frequency tuning over 15 GHz, and reconfigurable filter shape. This demonstration paves the way for implementing high-performance integrated photonic processing systems that merge complementary linear and nonlinear properties, for advanced functionality, enhanced performance, and compactness.