The capacity of a wireless lattice network with local interference is studied. In particular, the transport capacity under a multiple unicast traffic pattern is studied for a network of nodes placed on a hexagonal lattice. Different ways of handling broadcast and superposition lead to various communication models. In particular we consider models arising from the use of compute-and-forward/physical layer network coding. If neither broadcast nor superposition is exploited, the normalized transport capacity was previously shown to be between 1/3 and 2/5. In this work it is shown that exploiting either broadcast or superposition increases the capacity to at least 3/7, hence providing a strict improvement.