Covalent adaptable networks (CANs) relying on dynamic cross-links have been developed to make the cross-linked polymeric materials and composites degradable. However, due to the reversibility of dynamic bonds, the CANs and composites suffer accidental degradation and failure upon a certain stimulus (moisture, acid/base, reductant/oxidant, etc.) in the application environment. Herein, inspired by parallel circuits, interlocked covalent adaptable networks (ICANs) were prepared by one-pot reactions from epoxy monomers and two curing agents that contained different dynamic bonds of aromatic disulfide and aromatic imine bonds, resulting in dual dynamic parallel cross-links in homogeneous epoxy networks. The ICANs exhibited outstanding mechanical properties and improved stability, relying on the topological interlocking structure. The ICANs could be unlocked and became degradable only when two stimuli were both applied to completely break the cross-links of disulfide bonds and imine bonds. When applying ICANs as a matrix to form carbon fiber-reinforced polymer (CFRP) composites, the resulted CFRP inherited the interlocking properties from the ICANs, exhibiting improved stability and nondestructive recyclability. Maintaining the degradable properties, the interlocking structure of networks provided a facile way to optimize the stability of CANs and their composites.