As the regenerative mechanisms of biological organisms, self-healing provides useful functions for soft electronics or associated systems. However, there have been few examples of soft electronics where all components have self-healing properties while also ensuring compatibility between components to achieve multifunctional and resilient bio-integrated electronics. Here, we introduce a stretchable, biodegradable, self-healing conductor constructed by combination of two layers: (i) synthetic self-healing elastomer and (ii) self-healing conductive composite with additives. Abundant dynamic disulfide and hydrogen bonds of the elastomer and conductive composite enable rapid and complete recovery of electrical conductivity (~1000 siemens per centimeter) and stretchability (~500%) in response to repetitive damages, and chemical interactions of interpenetrated polymer chains of these components facilitate robust adhesion strength, even under extreme mechanical stress. System-level demonstration of soft, self-healing electronics with diagnostic/therapeutic functions for the urinary bladder validates the possibility for versatile, practical uses in biomedical research areas.