To explore the relationship between cutting force, vibration and surface roughness is of great significance to predict surface roughness. In this paper, the 64 all-factor experiments of milling 45 steel were conducted with the control variable method of three factors and four levels of cutting speed v, feed per tooth f_z and cutting depth a_p. The main cutting force, axial force, radial force and vibration were measured on line, and the corresponding average value, standard deviation and RMS values of cutting force were obtained. At the same time, the two-dimensional surface roughness R_a, three-dimensional roughness average S_a and RMS S_q were measured off-line. Then five distribution functions such as Normal distribution, Exponential distribution, Gamma distribution, Weibull distribution and Cauchy distribution were used to fit the sample data. The optimal distribution function was determined by AIC criteria, and the unknown parameters were estimated by maximum likelihood method. The five Copula functions such as Gaussian Copula, t-Copula, Frank Copula, Gumbel Copula, and Clayton Copula were used to fit the related structural forms between milling force, vibration, and roughness, and the optimal Copula function was selected according to the AIC criteria and the parameters are determined. Deriving from the optimal Copula function, the Kendall rank correlation coefficient τ was chosen as the evaluation index to analyze and compared the overall relativity between milling force and surface roughness. A mixed Copula function was constructed to analyze the tail correlation between milling force and surface roughness.