Niobium-based alloys are commonly used as superconductors in particle accelerators and fusion Tokamaks. However, magnets made of these alloys experience considerable radiation damage, particularly from helium transmutation products in nuclear reactors, which tend to aggregate at grain boundaries (GBs) and phase boundaries (PBs). This aggregation severely degrades the material's performance. Furthermore, niobium is highly prone to oxidation at high temperatures, further restricting its applications in extreme environments. Recent studies have demonstrated that Cu/Nb multilayer composites fabricated through accumulative roll bonding (ARB) exhibit high yield strength, acceptable ductility, and excellent radiation resistance, making them highly promising for nuclear industry applications. In Cu/Nb multilayer composites with fcc/bcc structures prepared via ARB, interfacial instability and strain concentration can occur during deformation due to the high three-dimensional incompatibility of heterophase interfaces. In this study, Cu/Nb polycrystalline multilayer composites were prepared using ARB. In situ tensile tests were conducted using SEM to investigate the slip transfer and blocking behaviors at the GBs and PBs. These behaviors were studied by observing the slip trace alignment and surface morphology continuity. Slip transfer behavior in Cu/Nb multilayer materials was elucidated through statistical analysis of the Luster-Morris parameter (m' = cosψcosκ,where ψ and κ represent the angles between the two slip plane normal directions and the two slip directions, respectively) and residual Burgers vector (Δb = | b_s2-b_s1|, where b_s2and b_s1 are the two unit Burgers vectors of the slip systems in sample coordinate system). In the Cu layer, slip transfer occurs at the GBs when m′ exceeds 0.77 and Δb is less than 0.029. In the Nb layer, slip transfer occurs when m′ exceeds 0.81 and Δb is less than 0.250. For the Cu/Nb PBs, slip transfer occurs when m′ exceeds 0.93 and Δb is less than 0.173. Notably, the minimum m′(m_{\mathrm{t}\mathrm{h},\mathrm{m}\mathrm{i}\mathrm{n}}^{\text{'}})and maximum Δb (Δb_{th, max}) for slip transfer at Cu GBs are lower than those at Nb GBs, indicating that slip transfer is more likely to occur at GBs in the Cu layer. The m_{\mathrm{t}\mathrm{h},\mathrm{m}\mathrm{i}\mathrm{n}}^{\text{'}} for slip transfer at Cu/Nb PBs is higher than that at both Cu and Nb GBs, whereas the Δb_{th, max} lies between the two types of GBs. This phenomenon can be attributed to the more complex structure, higher interface energy, and lower shear strength of Cu/Nb PBs than GBs. To achieve slip transfer across fcc/bcc PBs, a larger resolved shear stress is thermodynamically required; and kinetically, the slip systems on both sides of the PB must be closely aligned, corresponding to a higher m_{\mathrm{t}\mathrm{h},\mathrm{m}\mathrm{i}\mathrm{n}}^{\text{'}} and a moderate Δb_{th, max}.