We calculate the properties of isospin-asymmetric nuclear matter based on chiral nucleon-nucleon (NN) and three-nucleon (3N) interactions. To this end, we develop an improved normal-ordering framework that allows to include general 3N interactions starting from a plane-wave partial-wavedecomposed form. We present results for the energy per particle for general isospin asymmetries based on a set of different Hamiltonians, study their saturation properties, the incompressibility, symmetry energy, and also provide an analytic parametrization for the energy per particle as a function of density and isospin asymmetry.