Rapid integration of distributed energy resources (DERs) in active distribution networks (ADNs) necessitates advanced planning methods to optimally determine the size, site, and installation time of DERs. However, existing approaches often assume balanced networks and neglect health degradation of DER assets, limiting the accuracy and practicality of the planning results. This paper proposes a new planning method for utility-owned distributed generators (DGs) and energy storage systems (ESSs) in an unbalanced ADN considering asset health degradation. First, the three-phase branch flow is modeled for unbalanced characteristics of ADNs, and host DERs separately in different phases. Then, based on the Wiener degradation process, the aging path of each DG unit is modeled to estimate its available capacity along with service time; the ESS aging is modeled to reflect the degradation cost during charging and discharging. Finally, a copula-based stochastic programming method is presented considering the correlations between renewables and power demands. The inclusion of market volatility in electricity price uncertainty further enhances planning realism. Numerical case studies on an IEEE-34 bus three-phase ADN demonstrate the effectiveness and advantages of the proposed method.