The radiation emission of the He lines 1s3p ³ P₁ 1s² ¹ S₀ +h and 1s3p ¹ P₁ 1s² ¹ S₀ +h in dense optically thick and non-Maxwellian plasmas is found to be sensitive to higher multipole orders both for the radiation transitions and the collisional excitation cross sections. It is demonstrated that magnetic dipole and even quadrupole radiation transitions influence not only the absolute radiation line emission but also their qualitative evolution in dense plasmas. The proposed radiation model describes the He emission for low- and high-density plasmas and enables diagnostics under typical conditions of both magnetic and inertial fusion plasmas.