The present paper aims to study the reflection/transmission of two-dimensional plane elastic waves (quasi-longitudinal displacement waves) at the interface between a self-reinforced half-space and an orthotropic micropolar elastic solid half-space. Three kinds of coupled elastic waves are reflected in the orthotropic micropolar half-space, and two types of waves are transmitted in the self-reinforced medium. The phase velocities obtained in closed form depend upon the angle of propagation and material parameters. The boundary conditions at the interface of the two media are solved, and reflection/transmission coefficients are obtained using Cramer’s rule. Numerical examples are given, and dependence of the reflection/transmission coefficients on the incident angle has been shown graphically. Also, the comparisons between anisotropic and isotropic cases have been marked distinctly. The obtained results may be utilised for the interpretation and analysis of geophysical data.