The bioimpedances of tissues beyond the stratum corneum, which is the outermost layer of skin, contain crucial clinical information. Nevertheless, bioimpedance measurements of both the viable skin and the adipose tissue are not widely used, mainly because of the complex multilayered skin structure and the electrically insulating nature of the stratum corneum. Here, a theoretical framework is established for analyzing the impedances of multilayered tissues and, in particular, of skin. Then, strategies are determined for the system-level design of electrodes and electronics, which minimize 4-wire (or tetrapolar) measurement errors even in the presence of a top insulating tissue, thus enabling non-invasive characterizations of tissues beyond the stratum corneum. As an example, non-invasive measurements of bioimpedances of living tissues are demonstrated in the presence of parasitic impedances which are much (e.g., up to 350 times) higher than the bioimpedances of the living tissues beyond the stratum corneum, independently on extreme variations of the barrier (tape stripping) or of the skin-electrode contact impedances (sweat). The results can advance the development of bioimpedance systems for the characterization of viable skin and adipose tissues in several applications, including transdermal drug delivery and the assessment of skin cancer, obesity, dehydration, type 2 diabetes mellitus, cardiovascular risk, and multipotent adult stem cells.