On-line monitoring of depths of cut (DOC) is an essential way to avoid machining defects, such as over-cutting and machining chatter. Data-driven machine learning algorithm play a principal role to realize the monitor. However, deficient training data and un-interpretable algorithm made it difficult to application. Therefore, a physics-informed interpretable machine learning algorithm was proposed. Firstly, a physics simulation model was established with DOC, rotation speed and feed speed as its inputs and time-domain signals of milling force as its outputs. The output force signals were quantitatively presented by the characteristic values of time domain, frequency domain and waveform parameters. Secondly, six dimensionless characteristics, namely the kurtosis, skewness, waveform factor, peak factor, pulse factor and margin factor of the resultant milling force, were explored through sensitivity analysis method. They were sensitive to DOC but insensitive to milling force coefficient, speed and feed speed. Then, a quantitative relationship model between features and DOC was established by using the least squares linear regression algorithm, which has an intrinsic interpretability. The model was trained by a labeled 100 groups test data. The experiments show that the accuracy of the proposed model for DOC monitoring is greater than 90%.