Expressions for the Hall coefficients and magnetoresistance of a thin semiconductor layer at the boundary of a heterojunction in a transverse magnetic field are obtained using the quantum Liouville equation. The film temperature is selected so that quantum dimensional effects can be considered along the film thickness and Landau levels in the film plane are not considered, that is, in the film plane, the energy of charge carriers changes continuously. The effect of surface scattering of charge carriers is considered through diffuse-mirror Soffer boundary conditions. The dependence of Hall coefficients and magnetoresistance on magnetic field induction, electrochemical potential and roughness parameter is analyzed. Keywords: quantum Liouville equation, Soffer model, Hall coefficient, magnetoresistance coefficient, quantum triangular well.