BATS (BATched Sparse) codes are a class of efficient random linear network coding variation that has been studied for multihop wireless networks mostly in scenarios of a single communication flow. Towards sophisticated multi-flow network communications, we formulate a network utility maximization (NUM) problem that jointly optimizes the BATS code parameters of all the flows and network scheduling. The NUM problem adopts a batch-wise packet loss model that can be obtained from the network local statistics without any constraints on packet loss patterns. Moreover, the NUM problem allows a different number of recoded packets to be transmitted for different batches in a flow, which is called adaptive recoding. Due to both the probably nonconcave objective and the BATS code-related variables, the algorithms developed for the existing flow optimization problems cannot be applied directly to solve our NUM problem. We introduce a two-step algorithm to solve our NUM problem, where the first step solves the problem with nonadaptive recoding schemes, and the second step optimizes adaptive recoding hop-by-hop from upstream to downstream in each flow. We perform various numerical evaluations and simulations to verify the effectiveness and efficiency of the algorithm.