We integrate the key results of our previous studies [8, 9, 11], providing a unified view on multimessenger and multiband (dual-line) observations of inspiraling double neutron stars (DNSs) in our Galaxy. Future space-based gravitational wave (GW) detectors, such as LISA, TianQin, and Taiji, are poised to bridge the detection gap of tight DNSs with orbital periods of approximately 10 min, which remain challenging to detect with radio telescopes. Our investigation will first explore GW and radio follow-up detection capabilities for Galactic inspiraling DNSs. Furthermore, next-generation ground-based GW observatories, such as Cosmic Explorer and Einstein Telescope, which are projected to be operational in the mid-2030s concurrently with LISA, TianQin, and Taiji, are expected to detect high-frequency GWs emitted by spinning NSs. This development will advance the study of dual-line GWs from DNSs. We then focus on GW waveform modeling for the spinning NS in a tight DNS and consider its potential role in inferring binary geometry and NS physics parameters by dual-line GW detection.