Lithium-ion batteries have been widely used as enabling energy storage in many industrial fields. Accurate modeling and state estimation play fundamental roles in ensuring safe, reliable and efficient operation of lithium-ion battery systems. A physics-based electrochemical model (EM) is highly desirable for its inherent ability to push batteries to operate at their physical limits. For state-of-charge (SOC) estimation, the continuous capacity fade and resistance deterioration are more prone to erroneous estimation results. In this paper, trinal proportional-integral (PI) observers with a reduced physics-based EM are proposed to simultaneously estimate SOC, capacity and resistance for lithium-ion batteries. Firstly, a numerical solution for the employed model is derived. PI observers are then developed to realize the co-estimation of battery SOC, capacity and resistance. The moving-window ampere-hour counting technique and the iteration-approaching method are also incorporated for the estimation accuracy improvement. The robustness of the proposed approach against erroneous initial values, different battery cell aging levels and ambient temperatures is systematically evaluated, and the experimental results verify the effectiveness of the proposed method.