We study spin-scattering asymmetry at the interface of two ferromagnets (FMs) based on a half-metallic Co$_{2}$Fe$_{0.4}$Mn$_{0.6}$Si (CFMS)/CoFe interface. First-principles ballistic transport calculations based on Landauer formula for (001)-CoFe/CFMS/CoFe indicate strong spin-dependent conductance at the CFMS/CoFe interface, suggesting large interface spin-scattering asymmetry coefficient ($gamma$). Fully epitaxial current-perpendicular-to-plane giant magnetoresistance (CPP-GMR) pseudo spin-valve (PSV) devices involving CoFe/CFMS/Ag/CFMS/CoFe structures exhibit an enhancement in magnetoresistance output owing to the formation of the CFMS/CoFe interface at room temperature (RT). This is well reproduced qualitatively by a simulation based on a generalized two-current series-resistor model with taking the presence of $gamma$ at the CFMS/CoFe interface, half-metallicity of CFMS, and combinations of terminated atoms at the interfaces in the CPP-GMR PSV structure. We show direct evidence for large $gamma$ at a half-metallic FM/FM interface and its impact on CPP-GMR effect even at RT.