We consider a finite-field model for the wireless broadcast and additive interference network (WBAIN), both in the presence and absence of fading. We show that the single-source unicast capacity (with extension to multicast) of a WBAIN with or without fading can be upper bounded by the capacity of an equivalent broadcast erasure network. We further present a coding strategy for WBAINs with i.i.d. and uniform fading based on random linear coding at each node that achieves a rate differing from the upper bound by no more than O(1/q), where q is the field size. Using these results, we show that channel fading in conjunction with network coding can lead to large gains in the unicast (multicast) capacity as compared to no fading