We derive macroscopic unsaturated flow laws from a microscopic Stokes-Cahn-Hilliard system posed in a periodically perforated porous medium. The model describes incompressible two-phase flow with diffuse interfaces and incorporates capillary effects through a chemical potential associated with a logarithmic free energy. Our main result shows that, in the homogenization limit, the averaged velocity satisfies a Darcy-Korteweg law. The effective permeability tensor is determined solely by the pore geometry, as in the saturated Stokes case, while the driving force contains both the pressure gradient and the capillary force. Consequently, the resulting macroscopic law is not, in general, reducible to the classical Darcy-Buckingham form driven by a scalar hydraulic potential. Combining this Darcy-Korteweg law with the homogenized Cahn-Hilliard equation, we obtain a generalized Richards-type system. The proof combines two-scale convergence, periodic unfolding, and Tartar's oscillating test function method. The main analytical difficulties come from the nonlinear Korteweg force and the singular structure of the logarithmic potential. We establish uniform estimates for the chemical potential and the singular term, identify the nonlinear capillary force in the homogenization limit, and derive the effective cell problems for the permeability and diffusion tensors. These results provide a rigorous derivation of macroscopic unsaturated flow laws directly from pore-scale diffuse-interface dynamics with logarithmic free energy. This is a collaborative effort with Rone LEI (Tohoku University).