Although a well-established body of literature has examined electrophysiological muscle classification methods and systems, ways to enhance their transparency is still an important challenge and requires further study. In this work, a transparent semi-supervised electrophysiological muscle classification system which uses needle-detected EMG signals to classify muscles as normal, myopathic, or neurogenic is proposed. The electrophysiological muscle classification (EMC) problem is naturally formulated using multiple instance learning (MIL) and needs an adaptation of standard supervised classifiers for the purpose of training and evaluating bags of instances. Here, a novel MIL-based EMC system in which the muscle classifier uses predictions based on motor unit potentials (MUPs) to infer muscle labels is described. This system uses morphological, stability, near fiber and spectral MUP features. Quantitative results obtained from applying the proposed transparent system to four electrophysiologically different groups of muscles, composed of proximal and distal hand and leg muscles, resulted in an average classification accuracy of 95.85%. The findings show the superior and stable performance of the proposed EMC system compared to previous works using other supervised, semi-supervised and unsupervised methods.