<p>We develop a theoretical framework for wave transmission across a welded interface between an elastic half-space (ES, M1) and a transversely isotropic piezo-visco-thermoelastic solid featuring two-temperature and three-phase-lag effects (TPVS, M2). A time-harmonic plane P or SV wave incident from M1 generates two reflected modes and four quasi-transmitted modes in M2. Enforcing perfectly welded boundary conditions, we obtain closed-form amplitude (magnitude) ratios for all reflected and transmitted waves. These ratios depend on incident angle and frequency as well as on material parameters—including viscosity, anisotropy, piezoelectric coupling, two-temperature, and phase-lag constants. Using the amplitude ratios, we derive corresponding energy partitions (energy ratios) and present parametric diagrams that elucidate how viscosity redistributes energy among the reflected and transmitted modes in representative TPVS settings. Several special cases are reported to benchmark the formulation and to connect with known elastic, thermoelastic, and piezoelectric limits. The results provide insight into interfacial wave behavior in complex media and are relevant to applications in hydrology, subsurface characterization, and earthquake engineering.</p>