In this paper, we design matched filters for diffusive molecular communication systems taking into account the following impairments: signal-dependent diffusion noise, inter-symbol interference (ISI), and external interfering molecules. The receiver counts the number of observed molecules several times within one symbol interval and employs linear filtering to detect the transmitted data. We derive the optimal matched filter by maximizing the expected signal-to-interference-plus-noise ratio of the decision variable. Moreover, we show that for the special case of an ISI-free channel, the matched filter reduces to a simple sum detector and a correlator for the channel impulse response for the diffusion noise-limited and (external) interference-limited regimes, respectively. Our simulation results reveal that the proposed matched filter considerably outperforms the benchmark schemes available in literature, especially when ISI is severe.