The cable-driven exoskeleton system can provide long-distance power transmission for limb movement, simplify exoskeleton design and thus enhance the portability, flexibility, and wearable comfort. However, the cable-driven exoskeleton system contains many nonlinear dynamics because of the cable's elasticity and friction, which poses a great challenge for its accurate modeling and control. This article establishes an integrated model for double-cable-driven exoskeleton systems, which considers comprehensive friction dynamics including Coulomb, Stribeck, viscous, and asymmetric dynamics. To address the difficulties in the online identification induced by the cable-conduit configuration, a continuous piecewise linear neural network is used to reconstruct the friction dynamics and thus avoid the use of immeasurable intermediate variables. This allows the integrated model to be used for both mechanism analysis and online identification. To achieve parameter identification, a low-pass filter operation is applied to obtain the estimation error, and then a fixed-time adaptive parameter estimation scheme based on the estimation error is developed. Finally, experimental results demonstrate the validity of the developed model and the efficiency of the proposed parameter identification method.