Previous models of microwave limb brightening have omitted the alignment of spicules along supergranule boundaries, have neglected the high temperature sheath around spicules, and have assumed an interspicular medium which was averaged over chromospheric network and non-network regions. We present a model which includes these factors. By constraining the model to conform to results from earlier UV and optical studies we are effectively left with two free parameters: the temperature at the core of the spicules, Tsub(c)sub(o)sub(r)sub(e), and (at solar minimum), the interspicular chromospheric network density model of the lower transition zone. The absence of limb brightening at the short millimeter wavelengths implies Tsub(c)sub(o)sub(r)sub(e) approx. < 6000 k. Differences between the model and certain deconvolved observations near 9 mm are expected as a consequence of an extension of emission beyond the optical limb, predicted by the model, which affects the accuracy of the deconvolution technique. Unlike models which assume homogeous spicules in a random distribution, ours does not require an abnormally high spicule area.