Neural speech enhancement systems are typically trained with signal-based losses such as the signal-to-distortion ratio (SDR) or mean squared error (MSE). Although computationally efficient, these objectives disregard human auditory processing and may penalize imperceptible errors at the expense of features critical to speech intelligibility. To address this, we propose Co-SDR, a loss computed from the basilar membrane representations produced by CoNNear, a convolutional neural network simulating cochlear mechanics. We integrate this biophysically-informed objective into the training of a multi-channel speech enhancement system, compare it against conventional losses and analyze the influence of the number of simulated cochlear channels. Results show that in corporating cochlear processing priors during training directs the network to prioritize perceptually relevant speech components, yielding consistent improvements across objective speech intelligibility and signal fidelity metrics.