In this paper, we propose an HBV infection model with DNA-containing capsids and age structures in both the latent and infected compartments. We derive the basic reproduction number ${\mathrm{\Re }}_0$ and prove, via Lyapunov functions and LaSalle's invariance principle, that the global dynamics are fully determined by ${\mathrm{\Re }}_0$: viral clearance when ${\mathrm{\Re }}_0<1$ and endemic persistence when ${\mathrm{\Re }}_0>1$. The local stability of each equilibrium is rigorously established by employing linearization techniques and analyzing the associated characteristic equations. Compared to the previous age-structured HBV models without a latent compartment, our results reveal the significant impact of latent age structure on infection thresholds and disease progression.