Integrated stretchable devices, containing soft modules, rigid modules, and encapsulation modules, are of potential use in implantable bioelectronics and wearable devices. However, such systems often suffer from electrical deterioration due to debonding failure at the connection between rigid and soft modules induced by severe stress concentration, limiting their practical implementation. Here, we report a highly conductive and adhesive bilayer interface that can reliably connect soft-soft modules and soft-rigid modules together by simply pressing without conductive pastes. This interface configuration features a nanoscale styrene-ethylene-butylene-styrene (SEBS) elastomer layer and a SEBS-liquid metal (LM) composite layer. The top SEBS layer enables a strong adhesion with different modules. The connections between soft-soft and soft-rigid modules can be stretched to high strains of 400% and 250%, respectively. Coupling electron tunneling through an ultrathin SEBS layer with LM particle networks in a SEBS-LM composite layer renders continuous pathways for electrical conductivity. Such a bilayer interface exhibits a strain-insensitive high conductivity (3.7 × 105 S m-1) over a wide strain range from 0 to 680%, which can be facilely fabricated in a self-organized manner by sedimentation of LM particles. We present a proof-of-concept demonstration of this bilayer interface as an electrode, interconnect, and self-solder for monitoring physiological signals.