Electroporation electrodes are laminated to a permeable membrane to form an electrode membrane. Such an electrode membrane is useful for a continuous controlled delivery of a therapeutic agent through the skin or mucosa, when placed in direct contact with the skin or mucosa and by application of electric field pulses at specified intervals. An electrode membrane can be assembled such that it incorporates an iontophoretic electrode in the same device. This device can be jointly utilized for electroporation and iontophoretic drug delivery through the skin and mucosal membrane.