With the rise of Industry 5.0, collaborative assembly lines (CAL) attempt to combine human flexibility with cobots' precision and repeatability. We propose a bi-objective mixed-integer linear programming (MILP) formulation that simultaneously balances tasks, schedules operations, and selects the collaboration mode at each station. The model incorporates four types of human–cobot interaction: independent, sequential, supportive, and simultaneous, aiming to optimize two conflicting objectives: the total energy consumption of the line and its operational cost. Computational experiments were conducted on benchmark instances from the literature. Using the ε-constraint method, we generated Pareto fronts that reveal clear trade-offs between cost and energy efficiency. The results show that the model effectively uses the four collaboration modes as design choices: human independent stations dominate energy-oriented solutions, while cobot independent configurations are favored when reducing labor cost is prioritized, and the sequential, supportive, and simultaneous modes are employed when combining human flexibility with robotic precision improves performance. Overall, the proposed method supports decision-makers in selecting between human-only, cobot-intensive, and hybrid CAL configurations based on their cost and energy objectives.