The energy management system (EMS) of hybridization and electrification plays a pivotal role in improving the stability and cost-effectiveness of future vehicles. Existing efforts mainly concentrate on specific optimization targets, like fuel consumption, without sufficiently taking into account the degradation of on-board power sources. In this context, a novel multi-objective energy management strategy based on deep reinforcement learning is proposed for a hybrid electric vehicle (HEV), explicitly conscious of lithium-ion battery (LIB) wear. To be specific, this paper mainly contributes to three points. Firstly, a non-parametric reward function is introduced, for the first time, into the twin-delayed deep deterministic policy gradient (TD3) strategy, to facilitate the optimality and adaptability of the proposed energy management strategy and to mitigate the effort of parameter tuning. Then, to cope with the problem of state redundancy, state space refinement techniques are included in the proposed strategy. Finally, battery health is incorporated into this multi-objective energy management strategy. The efficacy of this framework is validated, in terms of training efficiency, optimality and adaptability, under various standard driving tests.