We obtain the maximal regularity for the mixed Dirichlet-conormal problem in cylindrical domains with time-dependent separations, which is the first of its kind. The boundary of the domain is assumed to be Reifenberg-flat and the separation is locally sufficiently close to a Lipschitz function of m variables, where m = 0, . . . , d − 2, with respect to the Hausdorff distance. We consider solutions in both L p -based Sobolev spaces and L q,p -based mixed-norm Sobolev spaces.