Dependent censoring can bias conventional survival analyses, while nonlinear covariate effects challenge interpretable Cox modeling. We propose a copula-based deep partially linear Cox model (CD-DPLCM) that jointly models event and censoring times using a Frank copula. Linear effects remain directly interpretable, whereas deep neural networks capture multivariate nonlinear effects. Baseline hazards are approximated by B-splines, and all components, including the dependence parameter, are estimated through full likelihood. We also develop efficient-score-based inference for the finite-dimensional parameters. Simulations assess estimation accuracy and uncertainty quantification across different sample sizes, censoring rates, dependence strengths, and nonlinear structures, with comparisons against conventional Cox and copula-based proportional hazards methods. The framework offers flexible and interpretable survival analysis when the independent-censoring assumption is untenable.