This paper studies a coupled suspension bridge system featuring a unilateral nonlinear coupling of positive-part type and distributed delay feedback acting on the velocity components. Under appropriate assumptions linking the instantaneous damping coefficients and the delay kernels, we prove well-posedness and exponential stability via a carefully designed Lyapunov functional and multiplier technique. This work extends the existing theory by treating, for the first time in this setting, the combined effect of nonlinear unilateral coupling and distributed delay feedback.