Energy-efficient scheduling is highly necessary for energy-intensive industries, such as glass, mould or chemical production. Inspired by a real-world glass-ceramics production process, this paper investigates a bi-criteria energy-efficient two-stage hybrid flow shop scheduling problem, in which parallel machines with eligibility are at stage 1 and a batch machine is at stage 2. The performance measures considered are makespan and total energy consumption. Time-of-use (TOU) electricity prices and different states of machines (working, idle and turnoff) are integrated. To tackle this problem, a mixed integer programming (MIP) is formulated, based on which an augmented ε-constraint (AUGMECON) method is adopted to obtain the exact Pareto front. A problem-tailored constructive heuristic method with local search strategy, a bi-objective tabu search algorithm and a bi-objective ant colony optimisation algorithm are developed to deal with medium- and large-scale problems. Extensive computational experiments are conducted, and a real-world case is solved. The results show effectiveness of the proposed methods, in particular the bi-objective tabu search.