Collaborative edge computing (CEC) is an emerging paradigm for heterogeneous devices to collaborate on edge computation jobs. For congestible links and computing units, delay-optimal forwarding and offloading for service chain tasks (e.g., DNN with vertical split) in CEC remains an open problem. In this paper, we formulate the service chain forwarding and offloading in CEC with arbitrary topology and heterogeneous transmission/computation capability, and aim to minimize the network aggregated cost. We consider congestion-aware nonlinear cost functions that cover various performance metrics and constraints, such as average queueing delay with limited processor capacity. We solve the non-convex optimization problem globally by analyzing the KKT condition and proposing a sufficiency optimality condition. We propose a polynomial-time distributed algorithm that converges to the global optimum. The algorithm adapts to changes in input rates and network topology, and can be implemented as an online algorithm. Numerical evaluation shows that our method significantly outperforms baselines in multiple network instances, especially in congested scenarios.