In this paper, we develop cross-layer techniques suitable for wireless sensor networks (WSNs) that are capable of multichannel access. More specifically, we propose energy and cross-layer aware routing schemes for multichannel access WSNs that account for radio, MAC contention, and network constraints. By doing so, we guarantee to meet data rate requirements of end-to-end flows while maximizing the network lifetime. When MAC contention constraints associated with the shared wireless medium are not included in routing formulations, routing solutions may not be feasible, in that the shared medium may not be able to support the required data rates of these flows. In this paper, we first derive three sets of sufficient conditions that ensure feasibility of data rates in multichannel access WSNs. Then, utilizing these sets, we devise three different MAC-aware routing optimization schemes, each aiming to maximize the network lifetime. Finally, we perform extensive simulation studies to evaluate and compare the performance of the proposed routing approaches under various network conditions.